OPTO-ELECTRONIC CLASS AB MICROWAVE POWER AMPLIFIER …

OPTO-ELECTRONIC CLASS AB MICROWAVE POWER AMPLIFIER USING

PHOTOCONDUCVIVE SWITCH TECHNOLOGY

________________________________________________________

A Dissertation

presented to

the Faculty of the Graduate School

University of Missouri-Columbia

________________________________________________________

In Partial Fulfillment

of the Requirement for the Degree

Doctor of Philosophy

________________________________________________________

by

CHIH-JUNG HUANG

Dr. Robert M. O’Connell, Dissertation Supervisor

AUGUST 2006

2

© copyright by Chih-Jung Huang All Rights Reserved

3

The undersigned, appointed by the Dean of the Graduate School, have examined the

dissertation entitled



Presented by Chih-Jung Huang

A candidate for the degree of Doctor of Philosophy

And hereby certify that their opinion it is worthy of acceptance.

______________________________________ Robert O’Connell, Ph.D. ______________________________________ William Nunnally, Ph.D. ______________________________________ Naz Islam, Ph.D. ______________________________________ Justin Legarsky, Ph.D. ______________________________________ H. R. Chandrasekhar, Ph.D.

ii

ACKNOWLEDGEMENTS

This dissertation as well as the entire Ph.D. process would not have been possible

without the help of many people.

First, I would like to thank my advisor, Dr. Robert M. O’Connell for his advice,

guidance, and encouragement during this research. Furthermore, thanks are extended to

all of my committee members, Dr. William Nunnally, Dr. Naz Islam, Dr. Justin Legarsky

and Dr. H. R. Chandrasekhar, for their review of the manuscript and valuable comments

along the way.

Secondly, I want to dedicate this dissertation to all my beloved family members

who have provided support during this entire process from thousands miles away in

Taiwan. Thank you for being part of it.

iii

TABLE OF CONTENTS

ACKNOWLEDGEMENTS …………………………………………………… ii

LIST OF TABLES ……………………………………………………………... v

LIST OF FIGURES ……………………………………………………………... vi

ABSTRACT ………………………………………………………….………….. x

Chapter

1. Introduction …………………………………………………………… 1

General description

Chapter summary

2. Literature Review ……………………………………………………... 5

Power amplifier

Opto-electronic (OE) Class AB push-pull microwave power amplifier at 10 GHz (X band)

Photoconductive semiconductor switches (PCSSs)

3. Theory of GaAs PCSS and OE Class AB Push-Pull PA ……………... 18

Theory of GaAs PCSS

OE Class AB push-pull power amplifier

OE Class AB push-pull power amplifier using stacking and multi-layer GaAs PCSSs

4. Simulation Results ……………………………………........................ 47

Physical modeling features and dark I-V characteristic

Intrinsic GaAs PCSS photoconductive performance

Discussion of simulation results

iv

OE Class AB push-pull PA performance

OE Class AB push-pull PA with multi-layer PCSS structures

5. Conclusion and Extension …………………………………………… 85

Conclusion

Extension

REFERENCE ………………………………………………………………….... 88

VITA …………………………………………………………………………… 95

v

LIST OF TABLES

Table Page

2.1 Property comparison of GaAs and Si ……………………………………...... 17

4.1 Characteristics of the PCSS as Vcc in Fig. 4.3 is varied …………………….. 60

4.2 Characteristics of the OE Class AB push-pull PA as Vcc in Fig. 4.10 is varied from 3 to 5 Volts. ……………………………………………….....

67

4.3 Characteristics of the OE Class AB push-pull PA with a peak optical intensity of 5*107 W/cm2………………………………………………….

70

4.4 Characteristics of the OE Class AB push-pull PA with a peak optical intensity of 3*107 W/cm2 …………………………………………………

71

4.5 Characteristics of a two-layer PCSS structure as Vcc in Fig. 4.15 is varied….

74

4.6 Characteristics of the OE Class AB push-pull PA using two-layer PCSSs as Vcc in Fig. 4.10 is varied from 7 to 11 Volts ……………………………...

76

4.7 Characteristics of a three-layer PCSS structure as Vcc in Fig. 4.3 is varied from 9 V to 21 V………………………………………………………......

78

4.8 Characteristics of the OE Class AB push-pull PA using three-layer PCSSs as Vcc in Fig. 4.10 is varied from 11 to 16 Volts………………………….

80

4.9 Characteristics of the OE Class AB push-pull PA using five-layer PCSSs as Vcc in Fig. 4.10 is set to 20 and 25 Volts………………………………….

83

vi

LIST OF FIGURES

Figure Page

1.1 Block diagram of a typical wireless transmitter and receiver module ……. 2

2.1 Class A power amplifier …………………………………………………... 6

2.2 Push-pull power amplifier ………………………………………………… 7

2.3 Improved push-pull power amplifier using transformers or baluns ………. 7

2.4 Opto-electronic (OE) Class AB push-pull microwave power amplifier ….. 10

2.5 A cross sectional view of a conventional HEMT device structure ……….. 12

2.6 Band diagram corresponding to the HEMT device structure of Fig. 2.5 …. 13

2.7 A cross sectional view of a HEM photoconductive detector ……………... 14

2.8 A plain photoconductive switch …………………………………………... 15

3.1 Different configurations of GaAs PCSS, (a) lateral PCSS, (b) planar PCSS, and (c) opposed contact PCSS …………………………………..

19

3.2 Two Schottky diodes were formed when the bias voltage is applied to the switch based on Fig. 3.1 (b) …………………………………………….

21

3.3 Energy level diagram for the DDSA compensation mechanism ………….. 22

3.4 Electric field dependence of electron drift velocity in GaAs ……………... 23

3.5 The energy band E-K diagram of GaAs shows the electron distribution in

different electric field; (a) E < 5KV / cm; (b) 5 KV / cm < E < 15 KV /cm; (c) E > 15 KV / cm ………………………………………………...

24

vii

3.6 (a) Negative differential resistivity (NDR), dρ/dE < 0, (b) A typical J-E plot for CCNDR with S-like curve and load line ……………………….

28

3.7 Formation of high current filament in a CCNDR; (a) a region with slightly

higher field, (b) a high current filament running along the field direction ………………………………………………………………...

29

3.8 The SI-GaAs photoconductive semiconductor switch (PCSS) in question.

The upper face is uniformly illuminated by 0.85 um wavelength laser pulses ……………………………………………………………………

31

3.9 A complementary pair or push-pull Class B PA ………………………….. 34

3.10 Transfer characteristic of the Class B push-pull PA ……………………… 35

3.11 Circuit with two diodes added forming a Class AB PA …………………... 35

3.12 Schematic of the optical portion of the test platform ……………………... 37

3.13 Schematic of the electrical portion (Class AB push-pull PA) of the test platform …………………………………………………………………

38

3.14 New schematic of an OE Class AB push-pull Microwave PA with PCSSs 40

3.15 Waveforms of an OE Class AB push-pull microwave PA with PCSS …… 41

3.16 OE Class AB push-pull microwave PA with stacked PCSSs……………... 44

3.17 Three layer GaAs PCSS structure…………………………………………. 44

3.18 Two-layer GaAs photoconductive semiconductor switch (PCSS). The

upper face is uniformly illuminated by 0.85 um wavelength laser pulses…………………………………………………………………….

46

4.1 Dark (no illumination) I-V data for the PCSS, showing: (a) negative

differential resistance between 0.05 and 0.2 volts, (b) avalanche breakdown above approximately 7.0 volts ……………………………..

50

viii

4.2 PCSS current-electric field characteristics, illustrating the increase in breakdown field with decreasing device width………………………….

51

4.3 Circuit used in the Mixedmode software program to study the photoconductive behavior of the PCSS ………………………………...

52

4.4 Triangular laser pulse train used to study the PCSS ……………………… 53

4.5 Photocurrent io(t) in Fig. 4.3: (a) output due to two laser pulses of the type

shown in Fig. 4.4, with Vcc set to seven different values, (b) expansion of the data shown in Fig. 4.5(a) between 4.5*10-11 and 6.0*10-11 s……

54

4.6 Electron and hole concentration corresponding to Fig. 4.5 with Vcc set to 2 Volts, and the transient time equal to, (a) dark (before illumination), (b) 10 ps, (c) 20 ps, (d) peak (25 ps), (e) 30 ps, (f) 40 ps, (g) 45 ps, (h) 50 ps, (i) 55 ps, (j) 60 ps, (left side: anode, right side: cathode)………………………………………………………………….

55

4.7 Test circuit photocurrents due to a single 50.0 ps-wide triangular optical

pulse, with PCSSs of different widths. Device electric field = 200 KV/cm and peak optical intensity = 4.0 x 107 W/cm2 ………………….

56

4.8 Electron and hole concentrations 100 ps into the transient for the data shown in Fig. 4.7. (a) 0.1 um, (b) 0.2 um, (c) 0.3 um, (d) 0.4 um, (e) 0.5 um, (f) 0.6 um, (g) 0.7 um, (h) 0.8 um, (i) 0.9 um, (j) 1.0 um. (left side: anode, right side: cathode)………………………………………………

58

4.9 Test circuit photocurrents for PCSS devices with heights varied from 1

um to 10 um. The width and depth of the PCSS device are 0.1 um and 3 um, respectively, with bias voltage Vcc of 4 V………………………….

58

4.10 OE Class AB push-pull microwave PA with PCSSs ……………………... 64

4.11 (a) Ideal output voltage waveform of our simulated OE Class AB push-pull microwave PA, (b) waveform of vo

2(t). ……………………………

65

4.12 Load voltage vo(t) in Fig. 4.10 with Vcc set to seven different values ……. 67

ix

4.13 Load voltage vo(t) in Fig. 4.10 when the peak optical intensity is 5*107 W/cm2 …………………………………………………………………...

69

4.14 Load voltage vo(t) in Fig. 4.10 when the peak optical intensity is 3*107 W/cm2 …………………………………………………………………...

70

4.15 Photocurrent io(t) in Fig. 4.3 due to a two-layer intrinsic GaAs PCSS structure as shown in Fig. 3.18: (a) output due to two laser pulses of the type shown in Fig. 4.4, with Vcc set to fourteen different values, (b) expansion of the data shown in Fig. 4.15(a) between 4.5*10-11 and 6.0*10-11 s………………………………………………………………..

72

4.16 Load voltage vo(t) in Fig. 4.10 when using two layer PCSS structures with Vcc set from 7 V to 14 V………………………………………………...

75

4.17 Photocurrent io(t) in Fig. 4.3 due to a three-layer intrinsic GaAs PCSS structure: (a) output due to two laser pulses of the type shown in Fig. 4.4, with Vcc set to thirteen different values, (b) expansion of the data shown in Fig. 4.17(a) between 4.5*10-11 and 6.0*10-11 s………………..

77

4.18 Load voltage vo(t) in Fig. 4.10 when using three layer PCSS structures with Vcc set from 11 V to 21 V………………………………………….

79

4.19 Five-layer GaAs photoconductive semiconductor switch (PCSS). The

upper face is uniformly illuminated by 0.85 um wavelength laser pulses…………………………………………………………………….

82

4.20 Load voltage vo(t) in Fig. 4.10 when using five-layer PCSS structures

with Vcc set to 20 V and 25 V and two perfect triangular waveforms with the frequency of 10 GHz…………………………………………...

83

x



Chih-Jung Huang

Dr. Robert M. O’Connell, Dissertation Supervisor

ABSTRACT

Next generation land-based, mobile, phased-array radar systems for battlefield

applications must meet constraints on volume, weight, power consumption, and data

processing capability that are currently not available. The most inefficient component in

a phased array radar system is the final power amplifier in each transmit-receive (TR)

module. More recent final power amplifiers for TR modules have been configured in the

Class AB or push-pull mode with a theoretical efficiency of 78.5% and an operational

efficiency of only 20% at x-band (8-12.5 GHz) frequency. Note that an efficiency of

10% requires ten times the radiated power to be generated and 90% of the delivered

energy to be removed as heat. In this dissertation, we present a new scheme of power

amplifier, in particular, an opto-electronic (OE) Class AB push-pull microwave power

amplifier. With this amplifier, 50.0 % of circuit efficiency and 2.2 Watts of output power

can be achieved at X-band (8-12.5 GHz) by utilizing a novel photoconductive

semiconductor switch (PCSS) based on intrinsic GaAs instead of the traditional

microwave transistors.

1

Chapter 1 Introduction

1.1 General description

With the developments in wireless systems, data communications,

telecommunications, and aerospace systems, the demand for improved microwave

communication capability has been continually increasing over the last decade. For

applications such as radar, scientists are trying to improve the state-of-the-art in system

architectures and to produce more compact and lighter systems with reduced power

requirements [1]. To achieve this goal, avoiding unnecessary power losses in order to

reduce the size of the heat sinks is an important issue.

Fig. 1.1 shows the block diagrams of a typical wireless transmitter and receiver

module [2]. The first stage of the transmitter is the modulator that is used to modulate the

baseband signal into an intermediate frequency. This intermediate frequency (IF) signal

is then shifted up in frequency to the desired RF frequency using a mixer. The mixer

operates by producing the sum and difference of the input IF signal frequency and the

frequency of a separate local oscillator (LO). In order to allow the sum frequency to pass,

while rejecting the much lower difference frequency, a bandpass filter (BPF) is utilized.

A power amplifier (PA) is used to increase the output power of the transmitter. Finally,

this baseband information is placed onto a high frequency sine wave carrier signal that

can be radiated by the antenna using a propagating electromagnetic plane wave. The

receiver of Fig. 1.1 can recover the transmitted baseband data by essentially reversing the

functions of the transmitter components.

2

TR Switch

Power amplifier

Antenna

Bandpass filterMixer

Local oscillator

Mixer

IF filter

Modulator

Low noise amplifier

Bandpass filter

Demodulator

IF filter

Signal processing circuit

IF amplifier

In microwave communications, including phased array radar systems, the major

source of inefficiency is the amplifier circuits in the transmit-receive or TR modules,

especially the power amplifier (PA), which is usually required in the final stage of the

transmitter module. The purpose of the PA in the module is to provide sufficient gain

and output power to meet the radar system output requirements. Typical output powers

may be on the order of 0.3 to 0.6 W for a handheld cellular phone, or in the range of 10 to

100 W for a base station transmitter. Other important parameters of the PAs are linearity

and operating frequency.

The capability of a PA depends highly on the performance of the microwave

transistors selected. In order to achieve high power output capability, the microwave

transistors need to have high breakdown voltage. Also, high operation frequency for the

microwave transistors is necessary because most modern wireless systems rely on RF or

microwave signals, usually in the UHF (100 MHz) to millimeter wave (30 GHz)

frequency range. RF or microwave signals offer wide bandwidths, and are able to

Fig. 1.1 Block diagram of a typical wireless transmitter and receiver module.

3

penetrate fog, dust, foliage, and even buildings and vehicles. Most of the microwave

transistors in use today are three terminal electrically controlled solid state devices such

as field effect transistors (FETs), hetrojunction bipolar transistors (HBTs), and high

electron mobility transistors (HEMTs) [2]. All these devices can be fabricated in

semiconductor materials such as Silicon (Si) and Gallium Arsenide (GaAs). Moreover,

microwave transistor PAs are characterized by low cost, they are reliable, and they can be

easily integrated in monolithic integrated circuits with other system components such as

mixers and oscillators.

In this dissertation, we present a new scheme of PA, in particular, an opto-

electronic (OE) Class AB push-pull microwave power amplifier. With this amplifier,

high circuit efficiency and reasonable output power can be achieved at X-band (8-12.5

GHz) by utilizing a novel photoconductive semiconductor switch (PCSS) based on

intrinsic GaAs instead of the traditional electrically controlled microwave transistors.

The objective of this project is to investigate and develop the new PA with an ultimate

goal of an efficiency of 60% at 10 GHz.

1.2 Chapter summary

The remainder of this dissertation contains four chapters. Chapter 2 is the

literature review. It describes previous related work by other researchers. Included is a

review of work on PCSSs and PAs that have relevance to our research. We will also

describe the state-of-the-art and the limitations of PCSSs and PAs today. Chapter 3

describes our research approach. It includes an analytical description of the semi-

4

insulating (SI) and intrinsic GaAs microwave PCSS and the OE Class AB push-pull PA

and a discussion of methods used in overcoming previous limitations. In addition, in

order to increase the output power capability at 10 GHz, a series and a multi-layer PCSS

structure will be described.

Chapter 4 contains our simulation results. It describes the software used for

simulation, and describes and analyzes the simulation results and compares them with

analytical results. Finally, Chapter 5 concludes the dissertation and also defines

continuation work that might be done in the future.

5

Chapter 2 Literature Review

We will divide this chapter into three sections. In the first section, we will discuss

different classes of power amplifiers and their limitations. In the second section, we will

explain why our OE Class AB push-pull PA promises to be better than others in some

specific ways at 10 GHz frequency. In the third section, we will review different

photoconductive semiconductor switches (PCSSs) and their applications.

2.1 Power amplifiers

Power amplifiers (PAs) are circuits for converting dc-input power into significant

amounts of RF or microwave output power. In most cases, PAs are not just small signal

amplifiers driven into saturation. There exists a great variety of PAs, and most employ

techniques beyond simple linear amplification [3]. According to the relations between

input and output RF microwave waveforms of the power amplifiers, we can divide them

into linear and nonlinear amplifiers. Class A, B and AB are linear power amplifiers, and

Class C, D, and E are nonlinear power amplifiers [4,5].

The Class A PA, shown in Fig. 2.1, has the best linearity among all PAs since the

Q (quiescent) point is selected to keep the transistor in its active region. Linearity is a

measure of the extent to which the output amplified waveform is identical in shape to that

of the input RF waveform. The RF choke (RFC) in Fig. 2.1 provides a constant DC input

current. The ideal collector-voltage and collector-current waveforms are sinusoids. The

Class A PA offers high gain, high linearity, and operation close to the maximum

6

operating frequency of the transistor. Here, gain can be defined as the average output

power divided by the input microwave average power.

micL PPG /= (2.1)

However, the theoretical efficiency of the Class A PA, defined as the average output

microwave power divided by the average DC input power, is very low, only 25% [4]; in

fact, previous systems initially employed Class A PAs with operating efficiency of only

10-12% at S-band [1] and above [6], a big disadvantage for our purposes.

The Class B or AB PA is also called a push-pull PA. A simple push-pull PA is

shown in Fig. 2.2 [7]. Note that it contains both NPN and PNP transistors. The gate bias

in an ideal push-pull PA is set at the threshold of conduction; therefore, each transistor is

active half of the time and its collector current is a half sinusoid. The push-pull PA also

provides good linear amplification because the output current is proportional to the gate

drive amplitude. However, the transconductance of the n-type transistor is an order of

magnitude greater than that of the p-type transistor due to the difference between electron

and hole mobilities, which limits the operating gain and efficiency of the push-pull pair.

Fig. 2.1 Class A power amplifier

Filter (Tuned circuit)

RFC

Vdc

RF input

7

Therefore, an improved push-pull PA, shown in Fig. 2.3, was developed, which requires

only n-type transistors [8,9]. Recently, the integrated-antenna concept was applied to

push-pull PA [10-14]. In this approach, the antenna serves as an out of phase power

combiner and tuned load for higher harmonics; thus, the output transformer or balun is

not required, which reduces power losses and increases circuit efficiency. A power

added efficiency (PAE) of 50 % has been demonstrated at an operating frequency of 3

GHz. However, at 5 GHz, the PAE drops to only 32 %. For microwave systems, the

power added efficiency (PAE) can be defined as

Fig. 2.3 Improved push-pull power amplifier using transformers or baluns.

Fig. 2.2 Push-pull power amplifier

8

smicL PPPPAE /)( −= (2.2)

where sP is the average input DC power, micP is the average input microwave power, and

LP is the average output power.) This loss in PAE is due to the limitations of the

transformer or balun. For the linear amplifiers, the Class AB PA shows better theoretical

efficiency, 78.5 %, than the class A PA, 25%.

Many applications do not require linear RF amplification and can therefore make

use of the greater efficiency offered by nonlinear Class C tuned power amplifiers [4].

The circuit topology of the classical Class C PA is the same as that of the Class A PA,

illustrated in Fig. 2.1. The active device is also driven to act as a current source.

However, the current waveform it produces is not the sinusoidal current desired in the

load because the gate of the Class C PA is biased below threshold, so that the transistor is

active less than half of the RF cycle. Thus, linearity is lost and a tuned output circuit

(tank circuit) or filter is needed in order to produce a sinusoidal signal at the load. The

theoretical efficiency of an ideal Class C PA is 100 %, and systems operating with PAE

of 50 % at 900 MHz have been demonstrated [15,16].

The Class D PA is also a nonlinear PA, which is very similar to the Class B and

Class AB PAs, shown in Fig. 2.2. The biggest difference is that the two transistors here

act as switches. A Class D amplifier employs a pair of active devices and a tuned output

circuit (tank circuit), which is not needed in the Class AB PA. The devices are driven to

act as a two-pole switch that defines either a rectangular voltage or rectangular current

waveform. The output circuit is tuned to the switching frequency and filters its

harmonics, resulting in a sinusoidal output. The efficiency of an ideal Class D PA is 100

%. However, because of switching, conduction, and gate drive losses of the transistors,

9

an efficiency of 90 % has been observed at only 14 MHz [17,18] and only 75 % at 900

MHz [19,20]. Again, the transformer or balun limits the Class D PA for use at high

frequency operation.

Similar to the Class C and D amplifiers, the Class E PA is another nonlinear PA.

The circuit setup for the Class E PA is similar to that of the Class A amplifier shown in

Fig. 2.1, but unlike the Class A PA, the transistor in the Class E PA is driven by a

rectangular input pulse [5]. Therefore, an output tank or tuned circuit is needed to filter

unwanted harmonics. In the ideal Class E PA, the collector voltage drops to zero and has

zero slope just as the transistor turns on, resulting in an ideal efficiency of 100 %.

However, the transistor switching losses reduce the circuit efficiency. Class E PAs have

been demonstrated with better PAE than other classes of PAs at different frequencies [21].

2.2 Opto-electronic (OE) Class AB push-pull microwave power amplifier at 10 GHz

(X band).

In wireless transmitter and receiver systems, size and efficiency are important

factors. In order to accomplish high circuit overall efficiency and power added efficiency

(PAE), a new scheme of PA, called an opto-electronic (OE) Class AB push-pull

microwave power amplifier, shown in Fig. 2.4, is proposed.

In this new scheme, optical input is used instead of electrical input, which leads to

several advantages of the system, the first of which is optical isolation of the input control

circuit from the main circuit. Switch control from a completely isolated source offers

multiple potential system benefits. Control source isolation and the ability to position the

10

controlling light beam will permit many sources to be applied to a single load or a single

source to be applied to multiple loads. Another advantage of using optical input is that

by using two optically controlled photoconductive semiconductor switches (PCSSs),

which are polarity independent, we eliminate the polarity issue described above. Thus,

higher efficiency should be achievable. Improving the efficiency will reduce the power

and thermal management requirements, which translate directly to the weight and volume

of the system. A third advantage is that, with optical illumination, an input matching

network, which is required when using an electrical RF input signal, is not necessary.

Class E PAs have been shown to have better PAE than Class AB (push-pull) PAs

at 10 GHz. For example, around 60 % circuit efficiency has been achieved in a Class E

PA at X band [22-24] versus only 20 % in a Class AB (push-pull) PA [25,26]. However,

in this project, an OE Class AB push-pull PA was chosen over an OE Class E PA for two

Fig. 2.4 Opto-electronic (OE) Class AB push-pull microwave power amplifier.

Light input

Light input

vL(t) iL(t)

+Vcc

-Vcc

ipcss1(t)

ipcss2(t) RL = 50Ω

PCSS1

PCSS2

+

-

11

reasons. The first reason is due to the simplicity of the input laser system. The input RF

microwave signal to be carried by the CW light laser can be produced relatively easily by

intensity modulating the light in the laser beam. This modulated light beam can be used

in our OE Class AB push-pull microwave PA because it is a linear amplifier. In contrast,

the Class E PA is a nonlinear amplifier which requires a rectangular light input pulse. It

is more difficult to produce a rectangular light pulse than to intensity modulate the light.

Therefore, the laser system is more complicated in the OE Class E PA. Secondly, due to

the nonlinear nature of the Class E PA, a tank (tuned) circuit is necessary and needs to be

well designed at the output stage of the amplifier in order to obtain a clean 10 GHz

sinusoid output waveform. The trade off to these advantages is that the theoretical circuit

efficiency for a Class AB PA is 78.5 % compared with the 100 % for the Class E PA.

2.3 Photoconductive semiconductor switches (PCSS)

In this section, electrically and optically controlled High Electron Mobility

Transistors or HEMT devices will be discussed first. We will explain why this device is

not suitable for our OE Class AB push-pull PA. Then, we will discuss photoconductive

semiconductor switches, which are attractive for our PA.

2.3.1 Electrically and optically controlled HEMT devices

Recently, electrically controlled HEMT devices have been popular in monolithic

microwave integrated circuits (MMICs) because of their high gain, low noise, and high

12

frequency response [27]. The HEMT is a heterostructure field effect device. The term

“High Electron Mobility Transistor” is applied to the device because the structure takes

advantage of the superior transport properties (high mobility and velocity) of electrons in

a potential well within lightly doped semiconductor material such as GaAs. It is also

called a Modulation Doped FET (MODFET).

Fig. 2.5 shows a cross-sectional view of a conventional HEMT device structure.

Note that a wide bandgap semiconductor material (n-type AlGaAs) lies on an undoped

narrow bandgap material (GaAs). AlGaAs and GaAs are the most common materials

used for this structure. The thickness and doping density of the AlGaAs layer are chosen

so that this layer is completely depleted of free electrons under normal operating

conditions.

Fig. 2.5 A cross sectional view of a conventional HEMT device structure.

n AlGaAs

Undoped GaAs

Semi-insulating GaAs

SOURCE DRAIN

GATE

2-DEG

n+ contact region

n+ contact region

Depletion region+

+

+

+

+

13

Fig. 2.6 shows the energy band diagram along the direction perpendicular to the

heterojunction interface using the AlGaAs/GaAs interface, i.e., along the dotted line in

Fig. 2.5. It shows that a sharp dip in the conduction band edge occurs in the HEMT at the

AlGaAs/GaAs boundary. This results in a high carrier concentration in a narrow region

along the GaAs side of the heterojunction. This high free-electron concentration is

described as a two-dimensional electron gas (2-DEG). Electrons traveling in this region

do not encounter ionized donor atoms because the GaAs is undoped. Therefore, ionized

impurity scattering effects are absent, so that the electron mobility is high and the device

has fast response time enabling high frequency operation [28].

Various papers have described the characteristics of electrically controlled HEMTs

with optical illumination to improve gain [29-33]. The results show the improvement of

the device gain due to the photoconductive and photovoltaic effects. However, these

electrically controlled HEMTs are not suitable for our OE Class AB push-pull PA design

Metal n AlGaAs GaAs

Ec

EF

2-DEG

Fig. 2.6 Band diagram corresponding to the HEMT device structure of Fig. 2.5.

14

because both p-type and n-type HEMT devices are still required. To eliminate this

problem, a HEM photoconductive detector, often called a metal-semiconductor-metal

photodetector, with a GaAs/AlGaAs/GaAs heterostructure, as shown in Fig. 2.7, was

considered [34,35]. Both drain and source contacts are formed as Schottky contacts.

When illuminated, electron and hole pairs generated in the GaAs layer exhibit an electric

field between drain and source; the increased charge increases the conductivity in the 2-

DEG layer. The response time, especially turn off time, depends on the thickness d of the

GaAs. If d is small, short turn off time can be observed. However, the trade off is that

the photogenerated current will be limited due to the absorption depth of GaAs. A turn

off or fall time of 22 ps has been achieved for d equal to 1 um as compared to 42 ps for d

equal to 2 um [34,35]. The 1 um device is fast enough for 10 GHz operation, but the gain

is too small because of the small value of d. The 2 um device is too slow. Thus, it was

concluded that this device is not suitable for our PA and a different active switch was

sought.

Fig. 2.7 A cross sectional view of a HEM photoconductive detector.

Undoped GaAs

n AlGaAs

Semi-insulating substrate

SOURCE DRAIN

2-DEG

Illumination

d

15

2.3.2 Photoconductive semiconductor switches (PCSSs)

Photoconductive semiconductor switches (PCSSs), as illustrated in Fig. 2.8, have

been shown to offer several advantages over conventional gas, mechanical, and

electrically triggered semiconductor switches. These include optical isolation of the

trigger, very low relative jitter, very fast switching speeds, simple mechanical structure,

extremely low inductance, and high thermal capacity [36-38]. Jitter of a conventional

switching system results from jitter of the electrical systems generating the trigger pulses

and from different switch closure times. The time delay between trigger pulse arrival and

switch closure initiation depends upon the availability of a free electron. Faster electrical

trigger pulse risetimes produce less jitter. Also, system jitter increases with the number

of switches to be closed. PCSS technology combines very fast closure with

subnanosecond delay, independence from circuit conditions, and very low jitter in switch

closure. These characteristics allow synchronizing many switches with very low jitter.

GaAs or Si. Ls

Anode

Cathode

Illumination

Fig. 2.8 A plain photoconductive switch.

16

PCSSs have been found to be useful in applications such as high voltage pulse

generation and high power microwave generation [39-41]. In such cases gain and power

are more important than speed of response, so the nonlinear avalanche-like lock-on effect

[42-44], which occurs when semi-insulating (SI) GaAs is biased above approximately 5.0

kV/cm, is used to produce gains more than 100 times larger than that possible with

operation in the linear mode [45,46]. The trade-off, of course, is that the device turn-off

or recovery time is substantially longer in the nonlinear mode as compared to the linear

mode [47,48]. Also, current filaments that occur during lock-on reduce the lifetime of

the PCSS [49,50]. Thus, lock-on must be avoided in PCSS devices designed for use at

GHz frequencies. Moreover, ways of increasing the breakdown strength of the PCSS are

necessary for high power applications. Studies have shown that opposed contacts with 20

um thick n+ layers can increase the breakdown field of a GaAs PCSS [40,51].

The physical properties of GaAs and Si are compared in Table 2.1. Compared

with GaAs, Si has lower fabrication process costs and higher stability of the devices that

are made from it; however, GaAs was selected for this project over Si for the following

reasons. First, GaAs has a larger bandgap than Si (approximately 1.42 eV compared with

1.12 eV for Si). The larger bandgap of GaAs results in much lower leakage current and

correspondingly higher dark resistivity. The dark resistivity of SI-GaAs is in the range of

107 to 108 Ω-cm [52]. Also, a larger bandgap also results in higher breakdown electric

field for GaAs. Furthermore, the maximum current density of GaAs is higher than in Si,

which reduces the chance of thermal run-away. Also, higher saturated drift velocity and

electron mobility for GaAs lead to higher photoconductive switch speeds than with Si.

17

Finally, GaAs is a direct bandgap material, so that the optical processes are much faster

than in the indirect bandgap material silicon.

Property Units Si GaAs Physical and Electronic

Bandgap at 300K eV 1.12 1.43 Thermal Conductivity W/cm-K 1.5 0.5 Saturated Drift Velocity cm/sec 1.0*107 2.0*107 Drift Mobility - Electrons cm/V-sec 1500 8500 Drift Mobility - Holes cm/V-sec 450 400 Max. Operating Surface Electric Field

KV/cm 90 150

Bulk Breakdown Electric Field KV/cm 200 300 Maximum Current Density KA/cm2 50 500 Maximum Current Per Unit Width KA/cm 0.5 500 Dielectric Constant - 11.8 12.8 Max. Junction Temperature ˚C ~250 ~300

In order to achieve our OE Class AB push-pull PA at 10 GHz frequency, a new

design of PCSS, which does not experience the lock-on effect, is needed. Since we have

a linear PA, the electrical output waveform must be able to follow the intensity of the

optical pulse; therefore, fast turn-on time and turn-off time are needed. In Chapter 3, we

will describe our new GaAs PCSS and OE Class AB push-pull PA.

Table 2.1 Property comparison of GaAs and Si.

18

Chapter 3 Theory of GaAs PCSS and OE Class AB Push-Pull PA

In this chapter, we will first discuss the characteristics and theory of our GaAs

PCSS. Then, we will apply our new GaAs PCSS design to our OE Class AB push-pull

PA, which we will discuss in the second section. In the third section, we will discuss

stacking and multi-layer GaAs PCSSs in order to increase the overall system output

power.

3.1 Theory of GaAs PCSS

A general description of GaAs PCSS devices will be given first in this section.

Also, we will discuss the GaAs PCSS physics. Finally, we will describe our new design

of GaAs PCSS, which is required to meet our specification for the OE Class AB Push-

Pull PA at 10 GHz (X band) operation.

3.1.1 GaAs PCSS device description

GaAs, a III-V compound semiconductor, is very popular for use in discrete and

integrated circuits for microwave, millimeter-wave, optoelectronic, and digital

applications. The resistivity of GaAs can be altered by illuminating the surface of the

material with an optical source whose photon energy is greater than the GaAs bandgap

energy. The absorbed photons generate electron-hole pairs with quantum efficiency near

19

unity. This effect, called photoconductivity, has been used for numerous applications,

principally in high speed photodetectors and high power switches.

Different choices of GaAs PCSS geometry have been studied for different

purposes [38,51]. Fig. 3.1 shows different GaAs geometries, including lateral PCSS,

planar PCSS, and opposed contact PCSS. The lateral PCSS, shown in Fig. 3.1(a), is the

simplest structure for coupling the optical energy into the switch. For uniformly

illuminated linear switching, the minimum resistance is reached almost immediately.

However, a disadvantage of this geometry is the exposure of the wafer surface to the full

electric field. For GaAs, the electric breakdown strength of a surface is usually

significantly lower (by approximately one-half) than the bulk electric breakdown strength

(Table 2.1). The planar PCSS, shown in Fig. 3.1(b), increases the breakdown voltage by

reducing fields near the switch surface. Similar to the lateral PCSS, light can be absorbed

in the active region and the lowest resistance can be achieved immediately. Finally, the

opposed contact PCSS shown in Fig. 3.1(c) was developed to improve the breakdown

voltage even further. With the same dimensions as for the planar and lateral PCSSs, the

opposed contact PCSS has higher breakdown voltage because the distance between the

Fig. 3.1 Different configurations of GaAs PCSS, (a) lateral PCSS, (b) planar PCSS, and (c) opposed contact PCSS.

i

contact

(a)

GaAs

contact

Illumination

i

contact

GaAs

(b)

contact

Illumination

i GaAs

contact

contact (c)

Illumination

20

two contacts is longer. However, the opposed contact PCSS is not suitable for X-band

microwave applications because the electrode distance needs to be short for high

frequency response. If that is the case, some of the optical power applied to the top

surface of the opposed contact PCSS may not be absorbed due to the shorter electrode

distance. Therefore, a planar GaAs PCSS (Fig. 3.1(b)) was chosen for our 10 GHz (X-

band) OE Class AB push-pull PA.

The two contacts of the PCSS can be either ohmic or Schottky contacts. To form

ohmic contacts, n+ layers need to be doped under the contacts; this forms electron

injection contacts. Thus, the contact injection efficiency is close to one, which also

improves the gain of the device. However, the trade-off of using ohmic contacts is that

the sweep-out time increases, meaning a longer turn off time. With Schottky or

rectifying contacts, since we do not have electron injection at the contacts, an increase in

the input optical power is required in order to compensate for the lack of electron

injection; therefore, we sacrifice gain in order to decrease the sweep out time (or reduce

the turn-off time). For our purposes, Schottky contacts are needed for the speed of

response required at 10 GHz.

In Fig. 3.1(b), Schottky contacts are placed on both sides of the semi-insulating

(SI) or intrinsic GaAs bulk material, which physically forms two Schottky diodes, as

shown in Fig. 3.2. Before illumination, the Schottky diode on the cathode end is forward

biased and the Schottky diode on the anode end is reversed biased so the device does not

conduct at small voltage. However, due to the small reverse breakdown strength of

Schottky diodes, current could start to flow at low voltage. For our switch, however,

current flow will be limited because of the high resistivity and breakdown voltage of the

21

semi-insulating (SI) or intrinsic GaAs bulk material, even though both Schottky diodes

can conduct. With illumination, large electron and hole concentrations decrease the

resistivity of the GaAs bulk material, so current can then flow through the device, turning

on the switch.

3.1.2 GaAs PCSS physics

Semi-insulating (SI) GaAs, just like intrinsic GaAs, has a high resistivity without

illumination. This results in very little leakage current when the switch is off. Single

crystals of semi-insulating or intrinsic GaAs have been grown by many techniques

utilizing melt and solution approaches, including horizontal Bridgman (HB) and vertical

Bridgman (VB), liquid-encapsulated Czochralski (LEC), liquid-encapsulated

Kyropoulous (LEK) and magnetic LEC (MLEC). The Bridgman technique is dominant

Anode Cathode

Illumination

SI-GaAs

i

Fig. 3.2 Two Schottky diodes were formed when the bias voltage is applied to the switch based on Fig. 3.1 (b).

22

in material quantity; however, the LEC-growth technique has become even more popular

since 1990 [27].

Different defects are associated with different growth techniques; therefore,

compensation mechanisms are usually required in order to produce the SI-GaAs material.

For example, SI-GaAs grown by the LEC method has one defect, called a deep donor

level EL2 trap. Experiments have shown that EL2 centers are electrically neutral when

occupied by electrons and they are positively charged when they release these electrons

[53,54]. Thus they behave like donors. For GaAs to exhibit semi-insulating behavior, a

shallow acceptor impurity, usually carbon (C) is doped to compensate the deep donor

EL2 defect. This is called the deep donor, shallow acceptor (DDSA) compensation

process. Fig. 3.3 shows the energy level diagram for this compensation mechanism.

For the PCSS shown in Fig. 3.1(b) based on SI-GaAs material with the DDSA

compensation mechanism or intrinsic GaAs, the electron is used as the majority carrier

because of its higher drift velocity and mobility compared with those of the hole.

According to the electric field dependence of electron drift velocity in GaAs, shown in

Fig. 3.4 [39], at low electric fields, generally smaller than 5 KV/cm, the electron drift

velocity is linear with the electric field, and it reaches its maximum, around 1.5*107

EL2

C

Ec

EvFig. 3.3 Energy level diagram for the DDSA compensation mechanism.

23

E

5 10 15 20 25 30 35 40 Electric Field (KV / cm)

0

3

6

9

12

15

Vd

Electron Drift V

elocity(10

6 cm / sec)

cm/sec, when the electric field is approximately 5 KV/cm. At higher electric fields, the

electron drift velocity decreases until the electric field is around 15 KV/cm, at which the

electron drift velocity reaches its saturated value around 7.7*106cm/sec. This happens

because of the nature of the energy band structure of GaAs.

Fig. 3.5 shows the energy band E-K diagram of GaAs. There are two valleys in

GaAs’s energy band, the upper valley and the lower valley. The energy difference

between them is around 0.31 eV. Electrons in the lower valley generally have higher

mobility than in the upper valley because they have lower effective mass in the lower

valley than in the higher valley. Under the influence of a small electric field, most of the

electrons stay in the lower valley shown in Fig. 3.5(a) and the electron drift velocity eυ

increases linearly with electric field. Thus, the electron mobility eµ is equal to

Ee

eυµ = . (3.1)

Fig. 3.4 Electric field dependence of electron drift velocity in GaAs.

24

As the electric field grows, those electrons in the lower valley obtain enough energy to

move into the upper valley shown in Fig. 3.5(b), where they have lower mobility. That is

why we see the velocity drop as the electric field becomes greater than 5 KV/cm. If the

electric field is increased further, most of the electrons will be in the upper valley as

shown in Fig. 3.5(c) and we will see almost constant drift velocity, as shown in Fig. 3.4.

The region where the electron drift velocity decreases with an increase in electric

field is called the region of negative differential mobility. In this region, the mobility is

equal to the derivative of the electron drift velocity with respect to the electric field

E

ee ∂

∂=

υµ (3.2)

Valance Band

Conduction Band

Eg

Lower Valley

∆E=0.31

Upper Valley

Conduction Band

Valance Band

[100] [111] 0 [111] 0 [100]

Valance Band

Conduction Band

[111] 0 [100]

Fig. 3.5 The energy band E-K diagram of GaAs shows the electron distribution in different electric field; (a) E < 5KV / cm; (b) 5 KV / cm < E < 15 KV /cm; (c) E > 15 KV / cm.

(a) (b) (c)

25

If the electric field is above 15 KV/cm, the electron drift velocities are constant at the

thermally limited saturation value sateυ , usually around 7.7*106 cm/sec. Thus, Equation

(3.1) becomes

Eesat

eυ

µ = (3.3)

and the carrier mobility varies inversely with the electric field. With higher electric field,

lower electron mobility can be expected.

As the bias voltage across the SI-GaAs PCSS shown in Fig. 3.1(b) is increased

from zero, the device goes through two modes of operation, beginning with the linear

mode. The linear mode is characterized by one electron hole pair produced by each

photon absorbed. Thus, the conductivity of the SI-GaAs PCSS is linearly proportional to

the total photon flux entering the device and the PCSS conductivity approximately

follows the variation of intensity of the optical pulse. The switch closes as the optical

intensity increases and the conductivity of the switch increases. The closure time of the

switch is determined by the rise time of the laser pulse. The switch turns off or opens

when the optical pulse is removed. The turn off time is determined by electron and hole

lifetimes, which are determined by various material and device parameters.

When the bias electric field across the switch exceeds approximately 4-8 KV/cm

[38], the transition occurs to a nonlinear mode that exhibits high gain and long

conduction times. This nonlinear mode is called controlled breakdown or lock-on. In

this mode, instead of following the light intensity pulse shape, the switch turns on and

stays on (lock-on) until the lock-on mechanism terminates. Some type of gain

mechanism occurs because there are many more carriers generated than can be created

26

directly by the incident photons. Furthermore, the switch continues to conduct for many

recombination times after the optical trigger has been removed. At present, lock-on

operation has only been found in GaAs and InP, which are both direct bandgap

semiconductors with a satellite valley in the conduction band that leads to negative

differential resistance (NDR). For bulk NDR, negative resistivity is associated with

microscopic bulk semiconductor properties, such as field-enhanced trapping, impact

ionization of shallow impurity levels in compensated semiconductors, and electron

transfer from a lower valley to higher valleys in the conduction band. A semiconductor

exhibiting bulk NDR is inherently unstable, because a random fluctuation of carrier

density at any point in the semiconductor produces a momentary space charge that grows

exponentially in time.

The physics of the lock-on effect is not well understood. One explanation of this

phenomenon is the so called field dependent trapping/de-trap phenomenon in SI-GaAs.

Using Fig. 3.3, consider the trap-to-band generation and recombination. At low field,

optical illumination excites the electrons in the EL2 trap to obtain enough energy to jump

to the conduction band; thus, the device turns on. When the optical pulse is removed,

electrons in the conduction band would stay for a period of time, called electron lifetime,

and then recombine with the trap. The electron life time, τe, can be determined by [55]

eτ = δυ **

1

etN (3.4)

where tN is the trap concentration, eυ is the average thermal velocity for electron, and δ

is the trap capture cross section area.

27

At high fields, approximately from 4-8 KV/cm, the trap capture cross section area,

δ, becomes larger than that at low field (field enhanced trapping). Therefore, the electron

lifetime time, τe, would decrease according to Equation (3.4) at high fields, which results

in shorter recombination time. Decreasing the recombination time also indicates that the

photo-generated electrons can get trapped easier at high fields compared with that at low

fields. The temporary increase of the device resistance due to the trap phenomenon

results in the temporary decrease of current. Instead of returning to the original carrier

concentration equilibrium (before illumination), the device would settle down with a new

steady state carrier concentration equilibrium because of the electron de-trap

phenomenon, due to impact ionization and trap-band tunneling. Therefore, lock-on

occurs.

Collective impact ionization and current controlled negative differential resistance

(CCNDR) have been studied to explain the current filaments observed in nonlinear SI-

GaAs PCSSs [56-58]. NDR devices can be classified into two groups: voltage controlled

NDR and current controlled NDR. Voltage controlled NDR devices include the tunnel

diode and transferred electron devices. Current controlled NDR can be found in thyristor

devices. Because of NDR, the semiconductor, initially homogeneous, becomes

electrically heterogeneous in an attempt to reach stability. Next, we will show that for a

SI-GaAs PCSS exhibiting CCNDR, high gain and high current filaments will form and

longer turn off time can be expected.

For CCNDR, the initial positive differential resistivity decreases with increasing

field; that is, dρ/dE < 0, as shown in Fig. 3.6(a). If a region of the device has a slightly

higher field, as shown in Fig 3.6(a), the resistance there is smaller. Thus, more current

28

will flow into it. This results in an elongation of the region along the current path, and

finally in the formation of a high current filament running along the field direction, as

shown in Fig. 3.7(b). The current filament usually is due to the carrier-carrier scattering

effect leading to collective impact ionization. Therefore, the avalanche-like lock-on

phenomenon leading to a high gain mechanism will be observed in nonlinear SI-GaAs

PCSS. Then, it will take substantially longer recovery time for the switch to return to its

normal state.

J1

J2

JX X

A (OFF)

B (ON)

J

E ET Emin

Load Line

Ebias

Fig. 3.6 (a) Negative differential resistivity (NDR), dρ/dE < 0, (b) A typical J-E plot for CCNDR with S-like curve and load line.

ρ

E ET (a)

(b)

29

Fig. 3.6(b) shows a typical instantaneous J-E plot and load line for a device with

CCNDR. This plot can also be used to explain the nonlinear operation of the SI-GaAs

PCSS. If the bias electric field, Ebias, is between the breakdown electric field, ET, and the

minimum lock on field, Emin, the dark current density (before illumination) is smaller

than J2 (see region A) and the device is in the OFF state. After the illumination is applied,

the optical trigger drives the system from the OFF state through the unstable state, Jx (or

region X), to the high current density state, J1 (region B), which is the ON state of the

switch. After the light trigger is removed, the device will stay ON because of the

avalanche process, and the electric field across the device will be at Emin, often called the

lock-on field. This situation will remain until the electrical signal across the switch is

removed.

3.1.3 Design features of SI-GaAs PCSS for X-band operation

-+

Region of slightly higher field

i

Low current density

High current region (filament)

+ -

Fig. 3.7 Formation of high current filament in a CCNDR; (a) a region with slightly higher field, (b) a high current filament running along the field direction.

30

As mentioned above, the nonlinear avalanche-like lock-on effect, which can occur

when semi-insulating (SI) GaAs is biased above approximately 5.0 kV/cm, is used to

produce gain more than 100 times larger than that possible with operation in the linear

mode. The trade-off is that the device turn-off or recovery time is substantially longer in

the nonlinear mode than in the linear mode. Thus, lock-on must be avoided in PCSS

devices designed for use at GHz frequencies. There are two ways to eliminate lock-on.

The first is to use intrinsic GaAs instead of SI GaAs; however, the trade off is that the

intrinsic GaAs is relatively harder to fabricate and more expensive than SI GaAs. The

other way is to use sweep-out mechanism instead of recombination to remove photo-

induced carriers if the lock-on phenomenon we discussed in the previous section is

accurate.

There are two ways to remove photo-generated carriers. The first way is to use

the natural recombination process of the material. For the switch and circuit to follow a

very fast falling optical signal, the switch recombination time must be less than or equal

to the falling optical signal. For our application, a 10 GHz optical pulse is a 1*10-10

second time pulse, which is faster than the electron and hole lifetimes of the SI-GaAs,

which are 5*10-10 sec. and 6*10-9 sec., respectively. Therefore, natural recombination is

not suitable for our problem. The second way is to use carrier movement to the

electrodes in the applied electric field of the conducting switch. The carriers move at

drift velocity and are removed at one electrode in a characteristic transit time. If the

carriers are not re-injected at the opposite Schottky contact as they are swept out of the

conducting region, they can be removed much faster than by natural recombination,

depending on the geometry of the switch. The sweep-out mechanism instead of natural

31

recombination can ideally prevent the lock-on phenomena as we discussed last section,

and also enable switch operation at X-band frequency.

The geometry of the designed PCSS is shown in Fig. 3.8. The material is LEC-

grown DDSA GaAs containing equal concentrations (3.0 x 1015/cm3) of deep lying EL2

traps and shallow carbon acceptors to simulate SI-GaAs. The electrodes are copper with

z (um)

y (um)

0.85 um wavelength laser pulses

0

3.0

10.0

0.1

Schottky Contacts (both y-z faces)

x (um)

d

Fig. 3.8 The SI-GaAs photoconductive semiconductor switch (PCSS) in question. The upper face is uniformly illuminated by 0.85 um wavelength laser pulses.

32

work function 4.7 eV to simulate rectifying Schottky contacts with extremely small dark

currents. The device is 10.0 µm tall, 3.0 µm deep, and only 0.1 µm wide in the direction

of photocurrent flow. The 10.0 µm device height was chosen to ensure band-to-band

absorption of at least 99% of the incident 0.85 µm wavelength light, whose absorption

coefficient in GaAs is approximately 5.0 x 103 cm-1. This is found by using the equation

yey αφφ −= *)( 0 (3.5)

where 0φ is the total photon flux (photon/cm2*sec) that enters the switch at y = 0, )(yφ is

the total photon flux in the switch at depth y, and α is the absorption coefficient of GaAs.

The 3.0 µm depth was chosen to provide a large enough cross-sectional area to

ensure that the photocurrent density would not exceed the 500 kA/cm2 allowable

maximum for GaAs, beyond which thermal runaway could occur.

Finally, the narrow 0.1 µm device width d (between the electrodes) was necessary

to ensure the fast removal of photocarriers by sweep-out in the electric field associated

with the applied voltage. This feature is necessary to minimize the probability of

collective impact ionization and subsequent lock-on during illumination, which would

render the device too slow for microwave applications. From ballistic transport theory

[27], when an electron encounters a sufficiently high electric field in a very narrow

region, it may not undergo the collisions needed to produce the steady-state speeds shown

in Fig. 3.4. Instead, higher velocities may be reached, resulting in shorter transit times.

At room temperature, the mean free path (m.f.p.) between collisions of an average

electron in GaAs is approximately 0.1 um. For this reason, 0.1 um was chosen as our

electrode separation distance.

33

3.2 Opto-electronic (OE) Class AB push-pull power amplifier

In this section, we will first describe the basic Class B and AB push-pull PAs.

Then, a hybrid experimental circuit that uses photodiodes and SiGe heterojunction

bipolar transistors (HBTs) developed by our group [59] will be described. The operation

frequency for this test platform ranged up to 4 GHz. Finally, the design of a fully OE

Class AB push-pull PA for 10 GHz operation will be described.

3.2.1 Basic circuit description of Class B and AB push-pull PAs

The purpose of the microwave PA is to amplify a high frequency sinusoid. Thus

the output voltage must also be a sinusoid, i.e., a signal having both positive and negative

values. One power amplification stage that can do this is called the “complementary-

pair” or “push-pull”, emitter follower configuration, also known as Class B PA, as shown

in Fig. 3.9. The active devices, Q1, and Q2, can be BJTs, MOSFETS, or HEMTS. When

the input signal is positive, the lower device, Q2, remains cut off, and the upper device,

Q1, is driven into the active region by the input signal. The large signal output for

positive input vin becomes that of a simple follower, that is,

vout = vin - Vf

Similarly, when the input is negative, the upper device, Q1, remains in cutoff, but the

lower device, Q2, is driven into the active region by the input signal. The output voltage

under such condition becomes,

vout = vin + Vf

34

Note that vout is equal to zero if the magnitude of vin is less than the base-emitter turn-on

voltage Vf.

Fig. 3.10 shows the complete transfer characteristic of the output stage, including

both positive and negative input voltages. Near the origin, where inv < Vf, the slope of

the transfer characteristic changes abruptly to nearly zero. This is called the crossover

distortion region. The crossover distortion illustrates the nonlinear behavior of the

amplifier and results in an output signal that is not an exact replica of the input signal.

The problem of crossover distortion in a Class B amplifier can be solved by

biasing the complementary-pair devices into the active region, just above cutoff. This

can be done with two diodes, as shown in Fig. 3.11. The diodes are kept forward biased

+-Vf

+-Vf

Fig. 3.9 A complementary pair or push-pull Class B PA.

35

Fig. 3.11 Circuit with two diodes added forming a Class AB PA.

Fig. 3.10 Transfer characteristic of the Class B push-pull PA.

36

by the bias network and the resistor R1. The series combination of D1 and D2 is

connected in parallel with the base-emitter junctions of Q1 and Q2 so that

VBE1 + VBE2 = VD1 + VD2 = 2Vf

where Vf is the turn-on voltage of the diodes.

D1 and D2 will behave as constant voltage sources of value Vf when an input

signal is applied. When vin is positive, Q1 will be driven into its active region, with vout

given by

vout = vin + VD1 – VBE1

= vin + Vf – Vf = vin (3.6)

When vin is negative, Q2 will be driven into its active region with vout given by

vout = vin - VD2 + VBE2

= vin - Vf + Vf = vin (3.7)

Thus, the problem of crossover distortion is eliminated by the use of the two biasing

diodes.

The price paid for reducing the crossover distortion is a small decrease in

amplifier power efficiency, due to the additional power loss in the diodes. This circuit is

often called the Class AB PA.

3.2.2 OE Class AB microwave amplifier test platform [59]

As mentioned in Chapter 2, the use of p-type and n-type transistor pairs is needed

to fashion a traditional Class AB push-pull PA because the polarity of the input electrical

37

signal is both positive and negative. However, the n-type transistor transconductance is

an order of magnitude greater than that of the p-type transistor due to the difference in

electron and hole mobilities, which limits the operating gain and efficiency of the push-

pull pair. One way to solve this problem is to use only n-type transistors. To

demonstrate the concept, we assembled a hybrid system consisting of photodiodes and

NPN SiGe heterojunction bipolar transistors (HBTs). The photodiodes were used

because optically gated SiGe HBTs are not currently available.

The hybrid table-top system consists of optical and electrical sections. Fig. 3.12

illustrates the optical portion of the system. The purpose of this section is to convert an

input optical signal to an electrical signal to drive the HBTs. The optical communication

standard OC-192 was used to design this section. The DFB laser diode shown in Fig.

3.12 was used to produce the optical power, which was modulated using the dual output

laser intensity modulator (LiNbO3 External Modulator). This produces two light beam

pulses at the output of the modulator that are 180˚ out of phase. The two pin photodiodes

were utilized to convert the optical power to electrical power. All of the optical

connections were linked by optical fibers.

Figure 3.12 Schematic of the optical portion of the test platform.

Electrical portion

38

Fig. 3.13 shows the electrical portion of the system, which is the Class AB push-

pull PA. The ideal inputs to the circuit are two electrical pulse trains coming from the

photodiodes in the optical portion of the system. These two electrical waveforms are

ideally positive and 180˚ out of phase. Therefore, two n-type SiGe HBTs could be used,

thereby eliminating the transconductance difference between n-type and p-type

transistors. SiGe HBTs were used for several reasons [59]. The first reason is because of

its high frequency operation capability. Second, they are compatible with silicon

technology, allowing the integration of logic functions. Third, the thermal conductivity

of SiGe is approximately three times higher than that of GaAs. Thus, thermal design of

the system is simpler. Finally, the cost of silicon-based devices is much lower than that

of GaAs FET devices.

The bias networks shown in Fig. 3.13 were needed in order to accurately drive the

two SiGe HBTs into the active region. We used –Vcc for the emitter DC power of HBT2

Fig. 3.13 Schematic of the electrical portion (Class AB push-pull PA) of the test platform.

vR(t) iR(t)

+Vcc

-Vcc

ic1(t)

ic2(t)RL=50Ω

Matching Network

Matching Network

Bias Network

Bias Network

SiGe HBT1

SiGe HBT2

Matching Network

From photodiode

39

in order to produce the negative portion of the sinusoidal waveform for the load voltage.

This circuit was built without input and output matching networks in order to study the

circuit over a range of frequencies. However, an amplifier built without input and output

matching networks will have reflection losses consuming 1/2 to 2/3 of the input power.

Thus, we expected the measured efficiencies to be much lower than the theoretical values.

A computer simulation study of the table-top system showed that up to 53 %

power added efficiency (PAE) can be achieved at 2 GHz, which is better performance

than the traditional Class AB PA. However, since matching networks were not included

in the experiment, the measured efficiency was only 14.1 % at 2 GHz, 8.5 % at 3 GHz,

and 2.9 % at 4 GHz. To improve the circuit operation, the laser diode needs to be

integrated with the laser intensity modulator and an integrated optical waveguide needs to

be used to connect the components, thus implementing it as a monolithic microwave

integrated circuit (MMIC). Also, matching networks need to be included in the MMIC to

reduce the reflection losses. Another way to improve the circuit is to utilize suitable

photoconductive semiconductor switches instead of the photodiodes and SiGe HBTS, as

discussed in the following section.

3.2.3 OE Class AB push-pull PA with our newly designed GaAs PCSSs

As explained in the previous section, an OE Class AB push-pull PA table-top test

platform was studied by our group. Photodiodes and SiGe HBTs were used at

frequencies up to 4 GHz. As Fig. 3.13 shows, the test platform was formed with HBT1

in the common-emitter mode in the upper branch and with HBT2 in the common-

40

collector or emitter follower mode in the lower branch. In this system arrangement, the

upper and lower branches are not symmetrical, which reduces the gain mechanism,

causing lower circuit efficiency. Thus, high efficiency operation at 10 GHz was not

possible for the table-top test platform. To improve matters, the photodiodes and HBTs

were replaced with photoconductive semiconductor switches (PCSS), as shown in Fig.

2.4 and repeated in Fig. 3.14 fro convenience. As mentioned in section 3.1.3, a properly

designed PCSS should be able to operate at 10 GHz. Also, the input matching network

and current controlled gate drive circuits needed for SiGe HBTs are eliminated since

there is no electrical signal before the PA, which reduces the complexity of the system.

The optical signals driving the photoswitches PCSS1 and PCSS2 are assumed to

be ultrafast laser pulses, which can be produced either by modulating the laser internally,

so that the laser produces the pulses directly, or by externally modulating the output

intensity of a continuous wave (CW) laser with a dual output Mach-Zehnder beam

Fig. 3.14 New schematic of an OE Class AB push-pull Microwave PA with PCSSs.

Optical pulse

Optical pulse

vo(t)

io(t)

+Vcc

-Vcc

ipcss1(t)

ipcss2(t) RL=50Ω

GaA

sPC

SS1 G

aAs

PCSS2

+

-

41

modulator, as was done in the hybrid system. In either case, the photoswitches are

assumed to be illuminated by a pair of laser optical pulse trains that are 180 degrees out

of phase with each other. Thus, to produce a 10.0 GHz output electrical signal vo(t), each

optical pulse train would consist of 50.0 ps-wide pulses with a 100.0 ps period. Fig. 3.15

shows the resulting photocurrents and output voltage. With the lower branch of Fig. 3.14

biased with negative Vcc as shown, the negative half-sinusoid of the output voltage is

generated. The output voltage and current can be written as

)sin(*)( wtVtv RR =

)sin(*)/()( wtRVti LRR = .

Therefore, the average output power PL can be found as

LP = >< )(*)( tvti RR

θ

ipcss1(t)

IR

ipcss2(t) θ

vR(t)

θ

-Ir

50 ps 100 ps

VR

-VR

Fig. 3.15 Waveforms of an OE Class AB push-pull Microwave PA with PCSS.

42

= >< )sin(*)/(*)sin(* wtRVwtV LRR

= >< )(sin*)/( 22 wtRV LR .

The time average of sin2(wt) is 0.5, so the average output power can be written as

LP = LR RV 2/2 . (3.8)

To calculate the average input power, the DC supply in the upper branch supplies

+sP = dttiVTT

pcsscc )(*/12/

01∫

= dtwtRVVTT

LRcc )sin(*/*/12/

0∫ .

Since ∫2/

0

)sin(T

dtwt = 2/w = T/π, we have

)/(*)/( LRccs RVVP π=+ .

The lower branch supplies the same average power. Therefore,

sP = )/(*)/2( LRcc RVV π (3.9)

and the efficiency of our circuit is

η = sL PP /

= )4/()*( ccR VV π . (3.10)

The maximum efficiency will occur when the resistance of the PCSS is zero (ideal case),

in which case VR = Vcc and equation (3.10) yields 78.5 % as the maximum efficiency for

the circuit. This is the same value as for the electrical Class AB PA.

With our new design of OE Class AB push-pull PA, higher practical circuit

efficiency at 10 GHz compared with the electrical Class AB circuits is expected because

43

the polarity and the transconductance problems are solved. Obviously, improving the

practical efficiency by a factor of 2 will reduce the power requirements and the thermal

management requirements by a factor of 2, which translate directly to the weight and

volume of the system. Also, the OE PA solves the isolation problem. Furthermore,

omitting the input matching network and gate drive circuits also increases the simplicity

of the circuit.

3.3 OE Class AB push-pull power amplifier using stacking and multi-layer GaAs

PCSSs

To produce greater output power levels, the input optical isolation should enable

several PCSSs to be stacked, as in Fig. 3.16, to allow use of a higher source voltage, Vcc,

which should lead to increased output power. Furthermore, since the ultimate goal of the

project is to produce a compact, fully integrated MMIC, the multi-layer GaAs

photoconductive switch shown in Fig. 3.17 is proposed. Using this structure instead of

stacking several PCSSs, higher breakdown voltages should also be achieved, which is

necessary to increase the output power of our new OE PA. Fig. 3.17 shows a three-layer

device in which each active layer would be 0.1 um thick as in the discrete PCSS; thus, the

device should operate well at 10 GHz frequency.

One expected problem with the stacked PCSS approach illustrated in Figs. 3.16

and 3.17 is that when we illuminate the multi-layer PCSS or stacked PCSS with the same

amount of peak optical intensity that was used in the single PCSS structure, the total on-

state voltage drop across the multi-layer PCSS or stacked PCSSs will be higher than that

44

+

-G

aAs

PCSS1

GaA

s PC

SS2 G

aAs

PCSS3

GaA

sPC

SS4

io(t)

vo(t)

RL=50Ω

ipcss1(t)

ipcss2(t)

+Vcc

-Vcc

Optical pulse

Optical pulse

Fig. 3.16 OE Class AB push-pull microwave PA with stacked PCSSs.

GaAs GaAs GaAs

Schottky contacts

Optical pulses

Fig. 3.17 Three layer GaAs PCSS structure.

45

of a single PCSS structure. The reason for this is that each PCSS has an on-state

resistance when illuminated; these on-state resistances will be in series, which will cause

the total on-state resistance to increase. Higher on-state resistance results in higher on-

state voltage drop across the PCSSs, which decreases the circuit efficiency.

There are two ways to solve this problem. The first method is to increase the

optical peak intensity in order to lower the on-state resistance of the multi-layer PCSS

structure. However, increasing the optical peak intensity will also increase the current

density in our PCSS which would increase the chance of the device thermal runaway.

Therefore, in order to reduce the device resistance and also maintain the maximum

allowable current density in the device, we suggest the second method, which is to

increase the device depth, z, shown in Fig. 3.8, while the individual layer or device width,

d, remains the same. According to the resistance versus resistivity relationship for a

semiconductor [60], as shown in equation (3.11), if we increase the effective electrode

width by using the multi-layer PCSS, we have to increase equally the same amount of the

current flowing area, A, in order to keeping the resistance constant. Increasing the device

depth, z, would accomplish that. This also maintains constant current density in the

PCSS, which avoids the thermal runaway problem.

AdR *ρ

= (3.11)

For example, Fig. 3.18 shows a two-layer GaAs PCSS structure with three

Schottly contacts located at x = 0, 0.1, and 0.2 um. In this case, the total device width d’

= 2d, ie 0.2 um. In order to maintain the same device resistance and current density

46

while using equal amounts of laser peak intensity, the device depth, z, needs to be

increased to 6 um instead of 3 um, as in a one layer PCSS device.

z (um)

y (um)


0

6.0

10.0

0.1

Schottky Contacts (three y-z faces)

x (um)

d’

0.2

Fig. 3.18 Two-layer GaAs photoconductive semiconductor switch (PCSS). The upper face is uniformly illuminated by 0.85 um wavelength laser pulses.

d d

47

Chapter 4 Simulation Results

In this chapter, simulation results obtained with the Atlas and Mixedmode

software packages available from Silvaco Inc [61] will be presented. Atlas is a physics-

based two-dimensional device simulator. It predicts the electrical behavior of user-

specified semiconductor structures, and it provides insight into the internal physical

mechanisms associated with device operation. Mixedmode is a circuit simulator that can

be used to simulate circuits that contain semiconductor devices for which accurate

compact models are unavailable, such as a device designed with Atlas.

The chapter is divided into five sections. In Section one, we discuss our intrinsic

GaAs PCSS design and the simulation result for the dark I-V characteristic, obtained with

Atlas software. In Section two, the photoconductive performance of the device, obtained

with Mixedmode software, will be described. In Section three, the results from Section

two will be discussed and analyzed. In Section four, the simulated performance of our

OE Class AB push-pull PA design, obtained using Mixedmode software, will be

presented. Finally, in Section five, the simulated performance of our OE Class AB push-

pull PA design with multi-layer PCSS structures will be presented.

4.1 Physical modeling features and dark I-V characteristic

In order to avoid the lock-on effect, two methods were discussed in Section 3.1.3.

However, since the Silvaco program does not support the lock-on effect (the physics of

lock-on is still unclear), we are unable to determine if our novel SI-GaAs PCSS design

48

can successfully eliminate the lock-on effect with the Silvaco software (see Chapter 5 for

the future extension). Therefore, for device and circuit studies with Silvaco software, our

PCSS, shown in Fig. 3.8, was assumed to be fabricated from liquid-encapsulated

Czochralski (LEC)-grown intrinsic GaAs instead of LEC-grown DDSA SI-GaAs

containing equal concentrations (3.0 x 1015/cm3) of deep lying EL2 traps and shallow

(carbon) acceptors. The electrodes are copper (work function 4.7 eV) to simulate

Schottky contacts with extremely small dark currents. The electron and hole lifetimes

were set to 5*10-10 sec and 6*10-9 sec, respectively [38].

In order to correctly simulate the device, proper models for carrier transport,

recombination, and avalanche must be included [62]. The carrier-carrier scattering effect

on mobility is needed when the carrier concentration is high. For modeling the velocity

saturation effect, parallel electric field dependent mobility must be included. Surface

dependent mobility and concentration dependent mobility were also included.

Recombination models are also important. The optical model in Atlas is utilized to

include band-to-band recombination. Auger recombination is also included because of

the potentially high current density in our device. Finally, the Schockley-Read-Hall

model is included to account for the trap-to-band recombination.

If a sufficiently high electric field exists within a device, local band bending may

be sufficient to allow electrons to tunnel, by internal field emission, from the valence

band into the conduction band [62]. Therefore, the band-to-band tunneling effect is also

included in our simulation. In the same manner, in a strong field, electrons can tunnel

through the bandgap via trap states; thus, trap-assisted tunneling is also included. Finally,

in any space charge region with a sufficiently high field, free carriers will acquire

49

sufficient energy to generate more free carriers when they collide with atoms of the

crystal. This is the avalanche effect, and it is included in the simulation using the impact

ionization model.

Fig. 4.1 shows the Atlas-software-determined variation of dark current with

anode-to-cathode voltage for the PCSS shown in Fig. 3.8. The peak current shown in Fig.

4.1(a) occurs at 0.05 volts, or 5.0 kV/cm. This point and the ensuing negative differential

resistance seen at higher voltages (electric fields) correlate, respectively and as expected,

with the peak and region of negative differential mobility observed in the field-dependent

behavior of electron drift velocities in GaAs, shown in Fig. 3.4. The approximately 4.3

pA constant anode current observed for voltages above approximately 0.3 volts or 30.0

kV/cm corresponds to the region where carriers are at their thermally limited constant

saturation velocities [39]. Fig. 4.1(b) shows the onset of avalanche breakdown at

approximately 7.0 volts, or 700.0 kV/cm, which is much higher than the bulk breakdown

field in GaAs, shown in Table 2.1. This gives us another benefit of the narrow PCSS

device width (0.1 um) besides a fast sweep-out charge removal time, as explained below.

Fig. 4.2 shows the PCSS current-electric field characteristics of PCSS devices

with different device widths. As can be seen, the breakdown field is independent of

device width and equal to the accepted value of approximately 300 kV/cm in GaAs for

device widths greater than approximately 1.0 µm. As the PCSS device width becomes

smaller than 1.0 µm, however, the breakdown field increases rapidly to approximately

twice the accepted value in the 0.1 µm device of interest. This result is presumably due

to the decreasing likelihood of the occurrence of the collisions needed to initiate the

avalanche process as the switch width approaches the mean free path between

50

0 0.2 0.4 0.6 0.8 1.0 1.2 1.40

1

2

3

4

5

6

7x 10

−12

Anode Voltage (V)

Ano

de C

urre

nt (

A)

(a)

3 4 5 6 70

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1x 10

−10

Anode Voltage (V)

Ano

de C

urre

nt (

A)

(b)

Fig. 4.1 Dark (no illumination) I-V data for the PCSS, showing: (a) negative differential resistance between 0.05 and 0.2 volts, (b) avalanche breakdown above approximately 7.0 volts.

51

collisions, which is approximately 0.1 um [27]. The significance of this result is that

amplifier output power is proportional to photocurrent, which in turn increases with

voltage across the PCSS. The larger breakdown fields shown in Fig. 4.2 mean that larger

voltages can be placed across the switch before prohibitive avalanche occurs.

4.2 Intrinsic GaAs PCSS photoconductive performance

To study the photoconductive behavior of the switch, Mixedmode software was

used to simulate its behavior in the simple amplifier circuit shown in Fig. 4.3. Note that

this is just the upper branch of our new OE Class AB PA shown in Fig. 2.4 and 3.14. As

0 100 200 300 400 500 600 7000

0.2

0.4

0.6

0.8

1

1.2x 10

−10

Electric Field (KV/cm)

Dar

k A

node

Cur

rent

(A

)

d = 0.1um

0.2 um

0.3 um

0.4 um

0.5 um

0.6 um 0.7 um

0.8 um

0.9 um

1 um

Fig. 4.2 PCSS current-electric field characteristics, illustrating the increase inbreakdown field with decreasing device width.

52

shown in Fig. 3.8, the entire upper surface of the switch was assumed to be uniformly

illuminated with 0.85 µm wavelength (1.45 eV photon energy) light to stimulate

photoconductivity via band-to-band absorption. As shown in Fig. 4.4, the light was

applied as a train of triangular pulses 50.0 ps wide and 100 ps apart or, equivalently, at a

pulse rate of 1010 per second (10.0 GHz). The triangular pulses were used to approximate

the DC-offset half-sinusoids that are produced by a laser modulator, but which are

difficult to simulate with the Silvaco software. Furthermore, it is easier to observe the

device turn-off delay time by using triangular pulses than other waveforms. The peak

intensity of the optical pulses was assumed to be 4.0 x 107 W/cm2, so that, considering the

0.1 µm by 3.0 µm device illumination area, the peak incident optical power was 0.12 W.

Laser diodes that emit this level of power at 0.85 µm wavelength are commercially

available [63]. The objective of the circuit illustrated in Fig. 4.3 is to produce a

photocurrent io(t) that in turn produces an output voltage vo(t) which replicates the

temporal intensity shape of the laser pulse train (triangular here) and which is as large as

vo(t)

Rpc(t)

Laser light intensity I(t)

Vcc

Photocurrent io(t)

+ -vpc(t)

+

-

PCSS

50Ω+

-

Fig. 4.3 Circuit used in the Mixedmode software program to study the photoconductive behavior of the PCSS.

53

possible. The capability of the circuit to do this was evaluated as a function of the dc bias

voltage Vcc.

Fig. 4.5 shows the temporal evolution of the photocurrent io(t) in Fig. 4.3 resulting

from light pulses of the type described above with the voltage Vcc in Fig. 4.3 set in turn to

0.5 V, 1.0 V, 2.0 V, 3.0 V, 4.0 V, 5.0 V, 6.0 V and 7.0 V. These curves illustrate an

important performance tradeoff. As can be seen, the output photocurrent tends to follow

the input triangular optical signal better as the bias voltage increases, but for values greater

than approximately 5.0 V, the recovery time of the photocurrent begins to increase

significantly beyond the 50.0 ps point required for 10.0 GHz operation, as the expanded

curves in Fig 4.5(b) clearly show. This is due to the onset of avalanche, which, as Fig.

4.1(b) shows, begins to occur at approximately 500 kV/cm or 5.0 volts in a 0.1 µm wide

device. This will be seen in later section to cause significant distortion in the output of the

OE Class AB amplifier. On the other hand, for the low bias voltages the photocurrent

I(t) (W/cm2)

t 0

4*107

25ps 50ps

λ = 0.85 um

100ps

. . .

Fig. 4.4 Triangular laser pulse train used to study the PCSS.

54

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 10−10

−0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

Transient time (s)

Phot

ocur

rent

io(t

) (A

)

0.5 V

1.0 V

2.0 V

3.0 V 4.0 V5.0 V 6.0 V

Vcc = 7.0 V

(a)

4.5 5 5.5 6

x 10−11

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Transient time (s)

Phot

ocur

rent

io(t

) (A

)

Vcc = 7 V

6 V

(b)

Fig. 4.5 Photocurrent io(t) in Fig. 4.3: (a) output due to two laser pulses of the typeshown in Fig. 4.4, with Vcc set to seven different values, (b) expansion of the datashown in Fig. 4.5(a) between 4.5*10-11 and 6.0*10-11 s.

55

decays to approximately zero in the 50.0 ps required for 10.0 GHz operation, probably

because there is little or no avalanche at those low voltages, but as can be seen in Fig.

4.5(a), it loses its triangular shape and becomes flatter and more square wave-like as the

bias voltage gets smaller. This is probably due to the current limiting effect of the 50

ohms resistor in Fig. 4.3. This is discussed in greater detail in Section 4.3.

Fig. 4.6 shows the electron and hole concentrations at several timer from zero to

60 ps throughout the transient for the Vcc = 2 volt data in Fig. 4.5. As can be seen, the

electron and hole concentrations reach their maxima when the optical intensity is at its

peak. When the optical pulse ends at 50 ps, there are still some residual electrons and

Loga

rithm

val

ues o

f ele

ctro

n (s

olid

line

) an

d ho

le (d

ashe

d lin

e) c

once

ntra

tion

Fig. 4.6 Electron and hole concentration corresponding to Fig. 4.5 with Vccset to 2 Volts, and the transient time equal to, (a) dark (before illumination),(b) 10 ps, (c) 20 ps, (d) peak (25 ps), (e) 30 ps, (f) 40 ps, (g) 45 ps, (h) 50 ps,(i) 55 ps, (j) 60 ps, (left side: anode, right side: cathode).

0 0.05 0.110

5

106

107

108

0 0.05 0.110

5

1010

1015

1020

0 0.05 0.110

5

1010

1015

1020

0 0.05 0.110

5

1010

1015

1020

0 0.05 0.110

5

1010

1015

1020

0 0.05 0.110

5

1010

1015

1020

0 0.05 0.110

5

1010

1015

1020

0 0.05 0.110

5

1010

1015

1020

0 0.05 0.110

5

106

107

108

0 0.05 0.110

5

106

107

108

(a) (b) (c) (d) (e)

(f) (g) (h) (i) (j)

PCSS width (um)

56

holes inside the PCSS device, as shown in Fig. 4.6(h). Fig. 4.6(i) shows that at 55 ps,

most of the electrons are swept out and the electron concentration is near dark

equilibrium value, shown in Fig. 4.6(a). However, since the holes are generally move

slower than electrons, they take longer (60 ps) to completely sweep out, as shown in Fig.

4.6(j).

To illustrate the importance of the width of the photoswitch, Fig. 4.7 shows test

circuit photocurrents due to a single light pulse of the type described above with PCSSs of

different widths between 0.1 µm and 1.0 µm. In each case the bias voltage was adjusted to

maintain the electric field across the device at 200 kV/cm, which is well below the

threshold for avalanche breakdown, and the optical power in the incident laser pulse was

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

x 10−10

−0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

Transient time (s)

Phot

ocur

rent

io(t

) (A

)

1 um 0.9 um 0.8 um

d = 0.1 um

0.7 um 0.6 um

0.5 um

0.4 um 0.3 um

0.2 um

Fig. 4.7 Test circuit photocurrents due to a single 50.0 ps-wide triangular optical pulse, with PCSSs of different widths. Device electric field = 200 KV/cm and peak optical intensity = 4.0 x 107 W/cm2.

57

adjusted to maintain the peak intensity at 4.0 x 107 W/cm2, as in Fig. 4.4. The data in Fig.

4.7 shows that although the peak photocurrent increases linearly with device width, the

signal is approximately able to track the 50.0 ps light pulse, which is essential for 10.0

GHz operation, only in the 0.1 µm wide device. The prohibitively increasingly longer

photocurrent decay times in the wider photoswitches are due to an increase in sweep-out

times resulting from greater distances between the electrodes, and a reduction of electron

velocities from high collision-less ballistic values in the 0.1 µm wide device (0.7 um is

approximately the mean free path between collisions) to lower saturated drift velocities

determined by electron-lattice collisions in wider devices. Thus, for 10.0 GHz operation,

it is necessary to sacrifice the gain evident in the wider devices for the required turn-off

speed.

Fig. 4.8 shows the electron and hole concentrations corresponding to Fig. 4.7 when

transient time is at 100 ps. As can be seen, at 100 ps, there are still relatively large carrier

concentrations for the devices with widths greater than 0.2 um. This result shows just how

critical the electrode separation is. The drastic difference in the photocurrent turn-off time

may in part be due to the occurrence of ballistic transport in the 0.1 um device because 0.1

um happens to be the mean free path (mfp) between electron collisions.

Fig. 4.9 shows the results of a parametric study of the PCSS device height. While

maintaining the same width and depth of our PCSS device, 0.1 um and 3 um, respectively,

and with bias voltage Vcc of 4 V, we varied the PCSS height from 1 um to 10 um. The

simulation results indicate that when the PCSS height is smaller than 4 um, the

photocurrent io(t) decreases dramatically because an increasing amount optical energy

cannot be absorbed by GaAs due to the absorption coefficient, as shown in Equation (3.5).

58

0 0.05 0.110

5

106

107

108

0 0.1 0.210

5

106

107

108

0 0.15 0.310

5

1010

1015

1020

0 0.2 0.410

5

1010

1015

1020

0 0.25 0.510

5

1010

1015

1020

0 0.3 0.610

5

1010

1015

1020

0 0.35 0.710

5

1010

1015

1020

0 0.4 0.810

5

1010

1015

1020

0 0.45 0.910

5

1010

1015

1020

0 0.5 110

5

1010

1015

1020

(a) (b) (c) (d) (e)

(f) (g) (h) (i) (j)

PCSSs widths (um)

Fig. 4.8 Electron and hole concentrations 100 ps into the transient for the data shown in Fig. 4.7. (a) 0.1 um, (b) 0.2 um, (c) 0.3 um, (d) 0.4 um, (e) 0.5 um, (f) 0.6 um, (g) 0.7 um, (h) 0.8 um, (i) 0.9 um, (j) 1.0 um. (left side: anode, right side: cathode)

Loga

rithm

val

ues o

f ele

ctro

n (s

olid

line

) and

ho

le (d

ashe

d lin

e) c

once

ntra

tion

0 0.5 1 1.5 2

x 10−10

−0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Transient time (s)

Phot

ocur

rent

io(t

) (A

)

y = 1 um

2 um 3 um

4 um 5 um − 10 um

Fig. 4.9 Test circuit photocurrents for PCSS devices with heights varied from 1 um to 10 um. The width and depth of the PCSS device are 0.1 um and 3 um, respectively, with bias voltageVcc of 4 V.

59

Changes in photocurrent become insignificant when the PCSS height equals 5 um or more

because most of the optical energy has been absorbed by the GaAs PCSS device.

4.3 Discussion of simulation results

To quantitatively interpret the data in Fig. 4.5, note in Fig. 4.3 that as the laser

light is absorbed by the PCSS, its diminishing resistance Rpc(t) determines the

photocurrent io(t), the voltage vpc(t) across the PCSS, and the output voltage vo(t) through

the equations

io(t) = Vcc/(Rpc(t) + 50) (4.1)

vpc(t) = Vcc – 50io(t) (4.2)

and vo(t) = 50io(t). (4.3)

As the light pulse increases in intensity from zero to its maximum value (4.0 x 107

W/cm2) and returns to zero, the switch resistance decreases from a very large off-state

value Rpc(max) to a minimum value Rpc(min) and returns to Rpc(max). Simultaneously,

photocurrent io(t) increases, as shown in Fig. 4.5 and according to Equation (4.1), to a

maximum io(max) and returns to zero. Given io(max) from the simulation data, Equation

(4.1) gives Rpc(min) as

Rpc(min) = [Vcc – 50io(max)]/io(max). (4.4)

Equations (4.2) and (4.3) show, respectively, that while the photocurrent rises and falls,

the switch voltage falls and rises, reaching a minimum value vpc(min) given by

vpc(min) = Vcc – 50io(max) (4.5)

60

and the output voltage rises and falls, reaching its maximum value vo(max) when the

photocurrent is maximum, i.e.,

vo(max) = 50io(max) (4.6)

The second, third, and fourth columns of Table 4.1 list, for each of the values of

Vcc considered in the simulations and given in the first column, the peak photocurrent

from Fig. 4.5(a) and the corresponding values of Rpc(min) and vpc(min) as determined with

Equations (4.4) and (4.5), respectively. The sixth column in the table lists the

corresponding ratios of vo(max) to Vcc, where vo(max) in the fifth column is determined

with Equation (4.6). This quantity represents the peak efficiency of the PCSS in

converting dc voltage to amplified signal (light intensity) voltage at the load. The final

two columns in Table 4.1 contain the maximum and minimum values of electric field

across the switch, E(max) and E(min), associated with, respectively, the corresponding

values of Vcc (vpc(t) in the absence of illumination) and vpc(min) listed in the first and

fourth columns. Note that for Vcc greater than 5.0 volts, E(max) is large enough to initiate

avalanche breakdown and increase photocurrent recovery time, as discussed above.

The data in Fig. 4.5 and Table 4.1 show that there are performance tradeoffs of the

amplifier/PCSS combination throughout the range of Vcc values considered. On one hand,

VCC (Volts)

io (max)(Amps)

Rpc (min) (Ohms)

vpc (min)(Volts)

vo (max)(Volts)

vo (max)/Vcc

E (max) (KV/cm)

E (min) (KV/cm)

0.5 1 2 3 4 5 6 7

0.00950.019 0.037 0.054 0.066 0.073 0.079 0.086

2.6 2.6 4.1 5.6

10.6 18.5 25.9 31.4

0.025 0.05 0.15 0.30 0.70 1.35 2.05 2.70

0.475 0.95 1.85 2.7 3.3 3.65 3.95 4.3

0.95 0.95 0.93 0.90 0.83 0.73 0.66 0.61

50 100 200 300 400 500 600 700

2.5 5.0

15.0 30.0 70.0 135 205 270

Table 4.1 Characteristics of the PCSS as Vcc in Fig. 4.3 is varied.

61

the peak efficiency of the circuit (the sixth column in Table 4.1) is quite high and

relatively constant for Vcc values below approximately 3.0 volts, but decreases rather

rapidly as Vcc increases beyond 3.0 volts. On the other hand, the photocurrents shown in

Fig. 4.5 are approximately triangular, i.e., undistorted, for the larger Vcc values where

circuit efficiency is relatively low, but they become increasingly rounded and flattened at

the small Vcc values where the efficiency is high.

The reduction in circuit efficiency as Vcc gets larger and the photocurrent

duplicates the shape of the laser pulse intensity with less and less distortion can be

explained in terms of the electric-field-dependent behavior of electron drift velocity in

GaAs, illustrated in Fig. 3.4. Since electron mobility is so much greater than hole mobility

in GaAs, the variation of the electrical resistivity ρ(t) (in ohm-cm) of the material during

illumination by the laser pulse can be approximated as

ρ(t) = [qn(t)µn(t)]-1 (4.7)

where q is the electron charge, n(t) is the concentration of photoelectrons, and µn(t) is

their mobility. Assuming that the laser intensity is small enough throughout the entire

pulse that the quantum efficiency for photocarrier generation is constant, n(t) essentially

follows the laser pulse intensity I(t), having a value n(max) at the peak of the laser pulse.

Thus, equation (4.7) indicates that ρ(t) is minimum with value ρ(min) at the peak of the

pulse. Assuming also that n(t) is never large enough to affect carrier mobility through

carrier-carrier scattering, µn(t) depends only on the instantaneous electric field and carrier

drift velocity through the relationship

µn(t) = vd(t)/E(t) (4.8)

62

As can be seen in Table 4.1, for Vcc greater than or equal to 2.0 volts, the electric field

across the switch is always at least 15.0 kV/cm, so that, as shown in Fig. 3.3, electron drift

velocities are constant at the thermally limited saturation value vsat. Thus, Equation (4.8)

becomes

µn(t) = vsat/E(t) (4.9)

and the carrier mobility varies inversely with the electric field during application of the

laser pulse, reaching a maximum value µn(max) when E(t) is minimum at the peak of the

laser pulse. Since E(min) increases with Vcc, µn(max) decreases accordingly. Thus, at the

peak of the laser pulse Equation (4.7) can be written as

ρ(min) = [qn(max)µn(max)]-1 (4.10)

If n(max) is relatively independent of Vcc when vd = vsat and µn(max) decreases with Vcc, it

is clear from Equation (4.10) that ρ(min) and thus Rpc(min) increase with Vcc when vd =

vsat, causing peak efficiency vo(max)/Vcc to drop, as shown in the table.

When Vcc is relatively small, i.e., 0.5 and 1.0 volts in Table 4.1, E(min) lies

approximately in the linear portion of the vd versus E data shown in Fig. 3.4, where the

electron mobility is roughly constant and much larger than it is when vd = vsat, as

discussed above. Thus µn(max) is independent of Vcc and much larger than in the

saturated drift velocity case, and Equation (4.10) shows that ρ(min) and thus Rpc(min) are

approximately constant and much smaller than in the saturated case, resulting in large and

constant peak efficiencies, as verified by the data in the table.

The rounding and flattening of the photocurrents shown in Fig. 4.5 when Vcc is

small and circuit efficiency is high can be explained in terms of the current limiting

behavior of the 50 ohm load. In the ideal case of zero minimum PCSS resistance during

63

illumination, Fig. 4.3 shows that the peak photocurrent io(max) would be equal to Vcc/50.

At the larger Vcc values, Vcc/50 is significantly larger than the corresponding io(max)

given in Table 4.1, suggesting that the circuit has little effect on the photocurrent,

allowing it to follow the temporal shape of I(t), as is the case in Fig. 4.5. At smaller

values of Vcc, Vcc/50 approaches io(max) given in Table 4.1, suggesting a growing current

limiting role by the circuit. At the smallest Vcc values, Vcc/50 and io(max) are nearly

identical, suggesting a strong current limiting role by the circuit. The extensive distortion

seen in the low Vcc traces in Fig. 4.5 support this.

The 0.1 um device data in Fig. 4.5 and Table 4.1 show that there is an optimum

range of Vcc values, between approximately 3.0 and 5.0 volts, for which the device

efficiency is reasonably high and the photocurrent is relatively undistorted, either by

circuit current limiting or by the onset of avalanche. The largest peak output voltage in

that window is 3.65 volts, corresponding to a peak output power of approximately 0.27

Watts. To try to improve this result, simulations were performed on a multi-layer PCSS

device which we will discuss in Section 4.5.

4.4 OE Class AB push-pull PA performance

Mixedmode software simulations were then performed with the new PCSS in the

OE Class AB push-pull power amplifier discussed in Chapter 3 and shown again in Fig.

4.10. The output matching network shown in Fig. 3.13 is omitted from Fig. 4.10 because

the Mixedmode software assumes that the circuit is well matched. Note that the amplifier

in Fig. 4.10 is just an expansion of the amplifier of Fig. 4.3 needed to produce the

64

negative half-cycle of the required 10 GHz sinusoid. The optical pulse trains indicated in

Fig. 4.10 are identical to that in Fig. 4.4 with the exception that the pulse train

illuminating PCSS2 is delayed by one-half cycle or 50 ps with respect to the pulse train

illuminating PCSS1.

The output and input power calculations of Chapter 3 were based on half-

sinusoidal optical pulse trains. Here, we derive the output and input powers associated

with triangular pulse trains. Fig. 4.11(a) shows the ideal output waveform of the PA in

Fig. 4.10 with half-triangular optical pulse train inputs. The instantaneous output power

can be written as

L

o

L

ooooo R

tvR

tvtvtitvtp

)()(*)()(*)()(

2

=== . (4.11)

The waveform of vo2(t) is shown in Fig. 4.11(b). From Equation (4.11), the average

output power Po can be calculated as

Fig. 4.10 OE Class AB push-pull microwave PA with PCSSs.

Optical triangular

pulse

Optical triangular

pulse

vo(t)

io(t)

+Vcc

-Vcc

ipcss1(t)

ipcss2(t) RL=50Ω

GaA

sPC

SS1 G

aAs

PCSS2

+

-

65

oP = ∫ dttpT o )(1 = ∫

2/

0

2 )(2/

11 T

oL

dttvTR

(4.12)

where ∫2/

0

2 )(2/

1 T

o dttvT

is the mean of the square of the triangular voltage waveform, which

is 3

2(max)oV

[64]. Therefore,

oP = L

o

RV

3

2(max) . (4.13)

At the input, the average power for one dc supply is equal to

+sP = dttiVTT

pcsscc )(*/12/

01∫

= dtR

tvVT

T

L

occ∫

2/

0

)(*/1

vo2(t)

T/2 T t

t

vo(t)

Vo(max)

-Vo(max)

Fig. 4.11 (a) Ideal output voltage waveform of our simulated OE Class AB push-pull microwave PA, (b) waveform of vo

2(t).

(a)

(b)

66

= ∫2/

0

)(*

T

oL

cc dttvRT

V (4.14)

where ∫2/

0

)(T

o dttv is the area of the triangular waveform; thus,

+sP = 2

*2*

*

(max)o

L

ccVT

RTV

= L

occ

RVV

4* (max) . (4.15)

Therefore, for two dc supplies

sP = L

occ

RVV

2* (max) . (4.16)

The efficiency of the circuit is, therefore,

η = so PP / = cc

o

VV3

2 (max) . (4.17)

The maximum efficiency will occur when the resistance of the PCSS is zero (ideal case)

in which case Vo(max) = Vcc; thus, the maximum efficiency for our simulated circuit is

66.7 %, which is smaller than the 78.5 % theoretical efficiency when sinusoidal optical

waveforms are used, as shown in section 3.2.3.

Figure 4.12 shows the simulation results of the load voltage vo(t) in Fig. 4.10

resulting from half-triangular optical pulses with peak value of 0.12 W and average power

of 0.06 W, with the voltage Vcc in Fig. 4.10 set in turn to 0.5 V, 1.0 V, 2.0 V, 3.0 V, 4.0 V,

5.0 V, 6.0 V and 7.0 V. The PCSS devices were 0.1 um wide. Similar to Fig. 4.5(a), the

curves in Fig. 4.12 are flattened and rounded in the low bias voltage cases, where current

limiting by the load is significant; they are increasingly distorted when the bias voltage is

67

large enough to cause significant avalanche; and they are approximately triangular (the

desired response) for a narrow range of bias voltages between approximately 3.0 V and

5.0 V.

Table 4.2 shows the important characteristics of the amplifier as a function of Vcc

for the three cases in Fig. 4.12 for which the output voltage is reasonably triangular and

VCC (Volts)

Vo(max) (Volts)

Popt (Watts)

Ps (Watts)

Po (Watts)

Efficiency(η,%)

Gain (dB)

PAE(%)

3 4 5

2.67 3.24 3.58

0.06 0.06 0.06

0.080 0.13 0.18

0.048 0.070 0.085

60.0 53.8 47.5

-1.9 1.3 3.0

N/A 3.2

14.0

Table 4.2 Characteristics of the OE Class AB push-pull PA as Vcc in Fig. 4.10 is varied from 3 to 5 Volts.

Fig. 4.12 Load voltage vo(t) in Fig. 4.10 with Vcc set to seven different values.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

x 10−10

−4−3.5

−3−2.5

−2−1.5

−1−0.5

00.5

11.5

22.5

33.5

4

Transient time (s)

Vcc = 0.5 V

1 V

2 V

3 V

4 V 5 V 6 V

7 V L

oad

volta

ge v

o(t)

(V)

68

the equations for the triangular approximation can be applied. Equations (4.13) and (4.16)

were used to find the output and input powers of the amplifier. The results are shown in

the fourth and fifth column of Table 4.2, respectively. The sixth column shows that the

resulting efficiency varies from 60.0 % to 47.5 %. The gain G of the circuit, given by

G = opt

o

PP , (4.18)

is given in db (G(dB) = 20 log (G)) in the seventh column of Table 4.2. The negative

gain observed when Vcc = 3 V occurs because Schottky contacts are used in the PCSS

design to prevent electron injection and improve device speed, which decreases the gain

of the PCSS. However, at Vcc = 5 V, a gain of 3 db is observed. The eighth column of

Table 4.2 shows the power added efficiency (PAE) of the circuit, where PAE is defined

as

PAE = s

opto

PPP )( −

. (4.19)

With negative gain, of course, the PAE is negative; thus, the PAE value for that case is

not given. Here, we idealize the insertion loss of the Mach-Zehnder beam modulator

equals to zero which gives us equal amount of the modulated output optical power, Popt,

and input microwave power of the modulator. In practice, the circuit PAE value will be

reduced due to the insertion loss of the optical modulator [65].

In order to examine the influence of peak optical intensity on the results,

simulations were performed with the peak optical intensity equal to 5.0 x 107 W/cm2 and

3.0 x 107 W/cm2. The results are shown in Fig 4.13 and Table 4.3 for the higher intensity

case and in Fig. 4.14 and Table 4.4 for the lower intensity case. The load voltage plots

show that signal distortion gets worse when optical intensity increases and it gets better

69

when the optical intensity decreases. The results reflect the fact that higher optical

intensities create more seed charge to participate in avalanche. Thus the signal distortion

gets worse and occurs at lower Vcc values as optical intensity increase. On the other hand,

the higher intensities cause smaller minimum resistances of the PCSS devices, which

leads to greater efficiency. This can be seen by comparing the efficiency values in Tables

4.2, 4.3, and 4.4 at Vcc = 4.0 volts, a value at which the output voltages in all three cases

are reasonably undistorted. As the optical intensity increases, efficiency increases but the

output voltage becomes increasingly distorted.

Fig. 4.13 Load voltage vo(t) in Fig. 4.10 when the peak optical intensity is5*107 W/cm2.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

x 10−10

−5−4.5

−4−3.5

−3−2.5

−2−1.5

−1−0.5

00.5

11.5

22.5

33.5

44.5

5

Transient time (s)

Vcc = 3 V

4 V

5 V

6 V

Loa

d vo

ltage

vo(

t) (V

)

70

VCC (Volts)

Vo(max) (Volts)

Popt (Watts)

Ps (Watts)

Po (Watts)

Efficiency(η,%)

Gain (db)

PAE(%)

3 4 5

2.78 3.55 4.00

0.075 0.075 0.075

0.083 0.14 0.20

0.052 0.084 0.105

62.7 60.0 52.5

-2.5 1.0 2.9

N/A 6.4

15.0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10−10

−4−3.5

−3−2.5

−2−1.5

−1−0.5

00.5

11.5

22.5

33.5

4

Transient time (s)

Vcc = 3 V 4 V 5 V

6 V

Loa

d vo

ltage

vo(

t) (V

)

Fig. 4.14 Load voltage vo(t) in Fig. 4.10 when the peak optical intensity is 3*107 W/cm2.

Table 4.3 Characteristics of the OE Class AB push-pull PA with a peak optical intensity of 5*107 W/cm2.

71

4.5 OE Class AB push-pull PA with multi-layer PCSS structures

As discussed in the previous section, when embedded our novel intrinsic-GaAs

PCSSs are used in the OE Class AB push-pull PA circuit, an optimum, intermediate value

of the bias voltage Vcc can be identified for which the amplifier is more than 50.0 %

efficient and produces 85 mW output power with very little distortion at 10 GHz. In

order to increase the output power, our PCSS device needs to be able to sustain higher

Vcc bias voltage. If we increase the width, d, of the PCSS (electrode distance), as shown

in Fig. 3.8, to increase the bias voltage, our analysis shows that the trade off of increasing

d would be the increase of the sweep-out time and the decrease of the breakdown field of

the device, as shown in Fig. 4.7 and Fig. 4.2, respectively. Alternatively, we could stack

several PCSS devices together in one multi-layer structure, in which, as discussed in

Section 3.3, higher output power levels can be expected without sacrificing the sweep-out

time and breakdown field of the device.

Fig. 4.15 shows the Mixedmode simulation result of the photocurrent io(t) in Fig.

4.3 by using a two-layer intrinsic GaAs PCSS structure, as shown in Fig. 3.18. The

VCC (Volts)

Vo(max) (Volts)

Popt (Watts)

Ps (Watts)

Po (Watts)

Efficiency (η,%)

Gain (db)

PAE(%)

3 4 5

2.39 2.69 2.86

0.045 0.045 0.045

0.072 0.11 0.14

0.038 0.048 0.055

52.8 43.6 39.3

-1.5 0.6 1.7

N/A2.7 7.1

Table 4.4 Characteristics of the OE Class AB push-pull PA with a peak optical intensity of 3*107 W/cm2.

72

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 10−10

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

Transient time (s)

Phot

ocur

rent

io(t

) (A

)Vcc = 14.0 V

13.0 V 12.0 V 11.0 V 10.0 V 9.0 V

8.0 V

7.0 V

6.0 V

5.0 V

4.0 V

3.0 V

2.0 V

1.0 V

(a)

4.5e−11 5.0e−11 5.5e−11 6.0e−110

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Transient time (s)

Phot

ocur

rent

io(t

) (A

)

Vcc = 14 V

Vcc = 13 V

Vcc = 12 V

Vcc = 11 V

(b)

Fig. 4.15 Photocurrent io(t) in Fig. 4.3 due to a two-layer intrinsic GaAs PCSS structure as shown in Fig. 3.18: (a) output due to two laser pulses of the type shown in Fig. 4.4, withVcc set to fourteen different values, (b) expansion of the data shown in Fig. 4.15(a) between4.5*10-11 and 6.0*10-11 s.

73

photocurrent io(t) is due to a triangular pulse train, as shown in Fig. 4.4, with the voltage

Vcc in Fig. 4.3 set in turn to 1 V to 14 V in increments of 1 V. In order to eliminate the

series resistance problem, the depth of the device was set to 6 um, as discussed in Section

3.3. For our two-layer device, we can successfully increase the Vcc to 14 V, which

corresponds to 700 KV/cm, which is the breakdown field of a single layer device.

Furthermore, the simulation results show the same trade-offs as discussed in Section 4.2.

The output photocurrent tends to follow the input triangular optical signal better as the

bias voltage increases, but for values greater than approximately 10.0 V, the sweep-out

time of the photocurrent begins to increase significantly beyond the 50.0 ps point required

for 10.0 GHz operation, as the expanded curves in Fig 4.15(b) clearly show. This is again

due to the onset of avalanche, which, as Fig. 4.1(b) shows, begins to occur at

approximately 500 kV/cm or 10.0 volts in a 0.2 µm wide device. On the other hand, for

the lower bias voltages, below approximately 6 V, the photocurrent loses its triangular

shape and becomes flatter and more square wave-like due to the current limiting role of

the load.

Table 4.5 shows the characteristics of a two-layer PCSS structure as Vcc in Fig.

4.15 is varied. Comparing it with the single layer PCSS case, summarized in Table 4.1,

the minimum PCSS resistance values, Rpc (min), listed in the third column of each table

agree with each other when both maximum electric fields across the device, E (max),

listed in the seventh column, are equal. For example, if E (max) equals 500 KV/cm, Rpc

(min) for a single layer PCSS is 18.50 ohms while Rpc (min) for a two-layer PCSS is 18.03

ohms. Corresponding minimum resistance values for both cases also yield similar peak

circuit efficiency listed in the sixth column. However, when E (max) equals 500 KV/cm,

74

io (max) and vo (max) increase from 0.073 A and 3.65 V, respectively, for a single layer

PCSS to 0.147 A and 7.35 V, respectively, for a two-layer PCSS. The reason for this

doubling of the circuit output current and voltage is that we are able to bias the two-layer

PCSS device with twice higher source voltage, Vcc, while also maintaining the same

minimum PCSS. This means higher output power can be expected with our two-layer

PCSS structure

Figure 4.16 shows the simulation results for the OE Class AB push-pull

microwave PA shown in Fig. 4.10 with our two-layer PCSSs. Results are shown for the

bias voltage Vcc set in turn to 7.0 V, 8.0 V, 9.0 V, 10.0 V, 11.0 V, 12.0 V, 13.0 V and 14.0

V. The lower voltage cases are not shown here because of the current limiting problem

shown in Fig. 4.15, which prevents the output voltage from replicating the input light

pulse. From Fig. 4.16, we see that when the bias voltage is large enough to cause

significant avalanche, the load voltage is increasingly distorted.

VCC (Volts)

io (max) (Amps)

Rpc (min) (Ohms)

vpc (min) (Volts)

vo (max) (Volts)

vo (max)/Vcc

E (max) (KV/cm)

E (min) (KV/cm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14

0.019 0.038 0.056 0.074 0.092 0.107 0.121 0.132 0.140 0.147 0.153 0.159 0.165 0.172

2.6 2.6 3.8 4.1 4.3 6.1 7.9

10.61 14.29 18.03 21.90 25.47 28.79 31.40

0.05 0.10 0.20 0.30 0.40 0.65 0.95 1.40 2.00 2.65 3.35 4.05 4.75 5.40

0.95 1.90 2.80 3.70 4.60 5.35 6.05 6.60 7.00 7.35 7.65 7.95 8.25 8.60

0.95 0.95 0.933 0.925 0.92 0.89 0.86 0.83 0.78 0.74 0.70 0.66 0.63 0.61

50 100 150 200 250 300 350 400 450 500 550 600 650 700

2.5 5.0

10.0 15.0 20.0 32.5 47.5 70.0 100.0 132.5 167.5 202.5 237.5 270.0

Table 4.5 Characteristics of a two-layer PCSS structure as Vcc in Fig. 4.15 is varied.

75


for the five cases in Fig. 4.16 for which the output voltage is reasonably triangular and the

equations for the triangular approximation can be applied. The third column shows that

the half-triangular optical pulses have peak power of 0.48 W and average power of 0.24 W

which is four times larger than in Table 4.2 for the single layer PCSS. This is because we

doubled both the width and the depth of our single-layer device to form the two-layer

device. This results in four times higher illuminated area, which requires four times

higher optical average power. Equations (4.13) and (4.16) were used to find the output

and input powers of the amplifier. The results are shown in the fourth and fifth columns

of Table 4.6, respectively. The results show that the output power of the amplifier with

two-layer PCSSs is also approximately four times larger than in the single-layer case. The

Fig. 4.16 Load voltage vo(t) in Fig. 4.10 when using two layer PCSS structures with Vcc set from 7 V to 14 V.

0 0.2e−10 0.4e−10 0.6e−10 0.8e−10 1e−10−8

−6

−4

−2

0

2

4

6

8

10

Transient time (s)

Loa

d vo

ltage

vo(

t) (

V)

Vcc = 14 V 13 V

12 V

11 V

7 V

8 V 9 V

10 V

76

reason for that is that we are able to double the circuit output voltage and according to

Equation (4.13), output power is proportional to the output voltage squared. This can be

seen by comparing Vcc = 5 V in Table 4.2 and Vcc = 10 V in Table 4.6. Finally, the sixth

column of Table 4.6 shows the efficiency of the amplifier. In the cases of reasonably low

signal distortion, i.e., for Vcc equals to 7 to 11 V, the efficiency of the circuit is 57.6 to

46.4 %, which is essentially the same as in the one-layer case. Therefore, with two-layer

device, we can increase the output power by a factor of 4 without sacrificing circuit

efficiency, gain, or PAE.

A similar simulation was conducted with a three-layer PCSS structure. In order to

eliminate the series resistance problem, the depth of the device was set to 9 um as

discussed in Section 3.3. Fig. 4.17 shows the Mixedmode simulation result of the

photocurrent io(t) in Fig. 4.3 when using a three-layer intrinsic GaAs PCSS structure. The

photocurrents io(t) result from a triangular optical pulse train and with the voltage Vcc in

Fig. 4.3 set in turn to 9 V to 21 V with the increment of 1 V. Here, we eliminate all the

voltages below 8 V due to the current limitation which flatters and makes the waveform

unusable. With a three-layer PCSS, the bias voltage Vcc can be increased to 21 V which

VCC (Volts)

Vo(max) (Volts)

Popt (Watts)

Ps (Watts)

Po (Watts)

Efficiency (η,%)

Gain (db)

PAE(%)

7 8 9

10 11

6.05 6.60 7.00 7.35 7.65

0.24 0.24 0.24 0.24 0.24

0.424 0.528 0.630 0.735 0.842

0.244 0.290 0.327 0.360 0.390

57.6 55.0 51.9 49.0 46.4

0.2 1.7 2.7 3.5 4.2

1.0 9.5 13.816.417.8

Table 4.6 Characteristics of the OE Class AB push-pull PA using two-layer PCSSs as Vccin Fig. 4.10 is varied from 7 to 11 Volts.

77

Fig. 4.17 Photocurrent io(t) in Fig. 4.3 due to a three-layer intrinsic GaAs PCSS structure: (a) output due to two laser pulses of the type shown in Fig. 4.4, with Vccset to thirteen different values, (b) expansion of the data shown in Fig. 4.17(a)between 4.5*10-11 and 6.0*10-11 s.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 10−10

−0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

Transient time (s)

Phot

ocur

rent

io(t

) (A

)Vcc = 21.0 V

20.0 V 19.0 V 18.0 V 17.0 V 16.0 V 15.0 V 14.0 V 13.0 V 12.0 V

11.0 V

10.0 V

9.0 V

(a)

4.5e−11 5.0e−11 5.5e−11 6.0e−110

0.02

0.04

0.06

0.08

0.1

0.12

Transient time (s)

Phot

ocur

rent

io(t

) (A

)

Vcc = 21 V

20 V

19 V

18 V

(b)

78

corresponds to 700 KV/cm breakdown voltage, again showing the agreement with a single

layer PCSS. Due to the onset of avalanche, as Fig. 4.1(b) shows, the recovery time of the

photocurrent begins to increase significantly beyond the 50.0 ps point required for 10.0

GHz operation at higher bias voltage.

Table 4.7 shows the characteristics of a three-layer PCSS structure as Vcc in Fig.

4.17 is varied. The results are similar to those for the single layer and double-layer PCSS

structures, shown in Table 4.1 and Table 4.5, respectively. For example, when the E

(max) equals 500 KV/cm, as listed in the seventh column for all three cases, the

minimum resistance, Rpc (min), listed in the third column and the circuit peak efficiency,

listed in the sixth column are similar, which again indicates that the multi-layer PCSS can

be utilized in our amplifier to obtain higher power.

VCC (Volts)

io (max) (Amps)

Rpc (min) (Ohms)

vpc (min) (Volts)

vo (max) (Volts)

vo (max)/Vcc

E (max) (KV/cm)

E (min) (KV/cm)

9 10 11 12 13 14 15 16 17 18 19 20 21

0.161 0.175 0.187 0.197 0.206 0.214 0.221 0.227 0.233 0.239 0.245 0.251 0.258

5.90 7.14 8.82 10.91 13.11 15.42 17.87 20.48 22.96 25.31 27.55 29.68 31.40

0.95 1.25 1.65 2.15 2.70 3.30 3.95 4.65 5.35 6.05 6.75 7.45 8.10

8.05 8.75 9.35 9.85 10.30 10.70 11.05 11.35 11.65 11.95 12.25 12.55 12.90

0.89 0.88 0.85 0.82 0.79 0.76 0.74 0.71 0.69 0.66 0.64 0.63 0.61

300 333 367 400 433 467 500 533 567 600 633 667 700

31.7 41.7 55.0 71.7 90.0 110.0 131.7 155.0 178.3 201.7 225.0 248.3 270.0

Table 4.7 Characteristics of a three-layer PCSS structure as Vcc in Fig. 4.3 is varied from 9 V to 21 V.

79

Figure 4.18 shows the simulation results for the OE Class AB push-pull

microwave PA shown in Fig. 4.10 when our three-layer PCSSs are used. Results are

shown for the bias voltage Vcc set from 11 V to 21 V. For the bias voltage above 17 V,

we observe that the load voltages are increasingly distorted because of the avalanche

effect.


for the six cases in Fig. 4.18 for which the output voltage is reasonably triangular and the

equations for the triangular approximation can be applied. The third column shows that

the peak optical power is now 1.08 W and the average optical power is now 0.54 W

because the illumination area of the device is now nine times the single-layer case. As

before, equations (4.13) and (4.16) were used to find the output and input powers of the

Fig. 4.18 Load voltage vo(t) in Fig. 4.10 when using three layer PCSS structures with Vcc set from 11 V to 21 V.

0 0.2e−10 0.4e−10 0.6e−10 0.8e−10 1e−10−15

−10

−5

0

5

10

15

Transient time (s)

Loa

d vo

ltage

vo(

t) (

V)

Vcc = 21 V 20 V 19 V

18 V

17 V

11 V

12 V 13 V

14 V 15 V 16 V

80

amplifier. The results are shown in the fourth and fifth column of Table 4.6, respectively.

Since three times more voltage can be applied in the PA circuit using three-layer PCSSs,

we are able to obtain approximately nine times more output power than by using single

layer PCSSs. In the cases of reasonably low signal distortion, i.e., for Vcc = 11 – 16 V,

the efficiency of the circuit is 56.7 to 47.3 %, which again is approximately the same with

in the one- and two-layer devices.

Our simulations show that the best linearity, efficiency, gain, and PAE always

occur for bias fields between 400 KV/cm and 500 KV/cm. Moreover, we can stack

layers in the PCSS in order to increase the output power of the circuit. However, there is

a limitation to the number of layers, which is the available average optical power of the

semiconductor laser. From our research [66], the highest CW semiconductor laser for the

wavelength of 850 nm is 3 W. Considering the modulator, the highest average output

laser power we can obtain is approximately 1.5 W. When we increase the layer structure

to five layers (PCSS width is 0.5 um), for maintaining the same current density inside the

PCSS, the depth of the device needs to increase to 15 um. This would increase the

illuminated area to 7.5 um2 keeping the peak optical intensity of 4*107 W/cm2, means we

VCC (Volts) Vo(max) (Volts)

Popt (Watts)

Ps (Watts)

Po (Watts)

Efficiency (η,%)

Gain (db)

PAE(%)

11 12 13 14 15 16

9.35 9.85 10.30 10.70 11.05 11.35

0.54 0.54 0.54 0.54 0.54 0.54

1.029 1.182 1.339 1.498 1.658 1.816

0.583 0.647 0.707 0.763 0.814 0.859

56.7 54.7 52.8 51.0 49.1 47.3

0.7 1.6 2.3 3.0 3.6 4.0

4.2 9.0 12.514.916.517.6

Table 4.8 Characteristics of the OE Class AB push-pull PA using three-layer PCSSs as Vcc in Fig. 4.10 is varied from 11 to 16 Volts.

81

would need a peak optical power of 3.0 W or average optical power of 1.5 W. Therefore,

we are limited to a maximum of five-layers in our PCSS structure.

Fig. 4.19 shows the five-layer PCSS structure. There are Schottky contacts in six

y-z faces at x = 0 um, 0.1 um, 0.2 um, 0.3 um, 0.4 um, and 0.5 um. The depth of the

PCSS increases to 15 um in order to maintain minimum resistance and limit the current

density of the device. The entire surface is illuminated by 0.85 um optical triangular

pulses as usual. Fig. 4.20 shows the Mixedmode simulation results of the output voltage

of the amplifier with five-layer PCSSs with bias voltages of 20 V and 25 V,

corresponding to 400 KV/cm and 500 KV/cm electric fields, respectively. Table 4.9

shows the important characteristics of the amplifier. For Vcc = 20 V and 25 V, the

efficiency of the circuit is 54.6 and 48.6 %, which are similar to the single layer, two-

layer and three-layer PCSS cases. The gain and PAE results are similar to other cases.

However, with the five-layer structure, we are able to increase the circuit average output

power to 1.79 W and 2.21 W when the Vcc is biased at 20 V and 25 V, respectively.

Fig. 4.20 also shows two perfect triangular waveforms at 10 GHz frequency. The

Waveform “A” has the same peak amplitude value as the Vcc = 20 V result and

Waveform “B” has the same peak amplitude value as the Vcc = 25 V result. Comparing

the corresponding pair of cases, we see that our amplifier can closely follow the rise-time

of the triangular pulse; however, the turn-off time is slightly slower than the fall time of

the triangular pulse, although our PCSS can still operate successfully at 10 GHz. The

reason for the slow turn-off time is that it still takes time for the photo-generated carriers

to sweep-out of the device even with the ballistic transport mechanism. Equation (4.18)

82

0.5 x (um)

y (um)

15.0

10.0

z (um)

Schottky Contacts (six y-z faces)

d

0


Fig. 4.19 Five-layer GaAs photoconductive semiconductor switch (PCSS). The upper face is uniformly illuminated by 0.85 um wavelength laser pulses.

83

was used in order to calculate the total harmonic distortion (THD) of our output

waveforms.

2,1

2,1

2

rms

rmsrms

VVV

THD−

= (4.18)

VCC (Volts)

Vo(max) (Volts)

Popt (Watts)

Ps (Watts)

Po (Watts)

Efficiency(η,%)

Gain (db)

PAE (%)

THD (%)

20 25

16.4 18.2

1.5 1.5

3.28 4.55

1.79 2.21

54.6 48.6

1.54 3.37

8.84 15.6

69 60

Table 4.9 Characteristics of the OE Class AB push-pull PA using five-layer PCSSs as Vcc in Fig. 4.10 is set to 20 and 25 Volts.

Fig. 4.20 Load voltage vo(t) in Fig. 4.10 when using five-layer PCSS structures with Vcc set to 20 V and 25 V and two perfect triangular waveforms with thefrequency of 10 GHz.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 10−10

−20

−15

−10

−5

0

5

10

15

20

Transient time (s)

Loa

d V

olta

ge V

o(t)

(V

)Vcc = 20 V

Vcc = 25V

Triangular Waveform "A"

Triangular Waveform "B"

84

Matlab software was used to find the Fourier series of the two amplifier load

voltage waveforms shown in Fig. 4.20. In addition, we also found the Fourier series of

the two perfect triangular waveforms. One hundred harmonic components were cal

culated. Therefore, Vrms and V1,rms for use in equation (4.18) were determined. The ninth

column of Table 4.9 shows the THD to be 69 % and 60 % for Vcc = 20 V and Vcc = 25 V,

respectively. Filtering circuit can be used to reduce the THD values.

85

Chapter 5 Conclusion and Extension

In this chapter, we will first summarize the important contribution of this

dissertation. Then, we will discuss the work than can be accomplished in the future in

order to improve upon the present results.

5.1 Conclusion

An intrinsic GaAs photoconductive switch that can operate at 10 GHz frequency

(X-band) has been designed and analyzed. The key feature of the switch is its narrow

(0.1 µm) width in the direction of current flow, which enables rapid removal of

photocarriers by sweep-out at carrier velocities greater than the saturated drift velocity.

The response of the PCSS to 50 ps wide triangular optical pulses at 10 GHz is limited at

low bias voltages by the current limiting behavior of the 50 ohm load resistance and at

sufficiently large bias voltages where the breakdown electric field of the semiconductor is

exceeded and avalanche begins, thus increasing the switch turn-off time. Thus, an

optimum, intermediate value of bias voltage exists where efficiency and distortion are

both reasonable and acceptable.

By using our novel PCSSs in a new OE Class AB PA, we have obtained simulated

efficiency value of 50 % at 10 GHz. The output signal is reasonably undistorted with an

average power between 50 and 85 mW. In addition, by using optical illumination, input

matching networks, which are required when using electrical RF input signals, are not

necessary, thereby reducing the complexity of the new amplifier. Another advantage of

86

using our new EO PA is the isolation of the input optical circuit from the main PA circuit,

which allows us to stack several PCSS devices together to form an equivalent multi-layer

PCSS. This should make it possible to use higher Vcc values, which would lead to

increased output power. Simulations showed that the OE Class AB PA with five-layer

PCSS devices can produce an average microwave output power of 2.2 W at 10 GHz while

maintaining a circuit efficiency around 50 %. The observed efficiencies of the new

optoelectronic amplifier represent an improvement over currently available, electronically

driven X-band microwave amplifiers. This result and the relative simplicity of the

amplifier should contribute to the development of compact, light-weight, mobile phased

array radar systems.

5.2 Extension

More parametric simulation on PCSS device heights will be studied. We will

make the on-state resistance in the PCSS more uniformly distributed by reducing the

PCSS height to from 10 um to 2 um. In addition, in order to test the accuracy of

PCSS/OE amplifier simulations, intrinsic GaAs PCSS devices need to be fabricated and

tested, including multi-layer structures. Fabricating the Schottky contacts may be a

challenge. Furthermore, in order to test the lock-on theory we proposed in Section 3.1.2,

devices made with semi-insulating GaAs PCSS need to be fabricated and tested. Next,

we will simulate our OE Class AB PA with sinusoidal optical waveform instead of the

triangular optical pulse. Then, our OE Class AB PA must be built and tested. For

improve the THD value we showed in Section 4.5, a filter will be required at the output

87

of the PA. Finally, the ultimate goal of this project is to produce a compact, fully

integrated MMIC power amplifier circuit at X-band operation that can be utilized to

produce more compact and lighter microwave systems.

88

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95

VITA

Chih-Jung Jerome Huang was born in Taipei, the capital city of Taiwan, on July

30, 1974. After attending public schools in Taipei, he received his junior college diploma

in the field of Electronic Engineering from the Kuang-Wu Junior College of Technology

in 1994. After graduating from the junior college, he attended the Air Force serving as

the Sergeant position in Hualien, Taiwan. After two-year military service, he came to

United State of America and attended the University of Missouri in Columbia to continue

his study in Electrical and Computer Engineering. He received his B.S. and M.S. degrees

in 1999 and 2001, respectively. He earned his Ph.D. degree in August 2006.

OPTO-ELECTRONIC CLASS AB MICROWAVE POWER AMPLIFIER …

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